Skip to main content\(\require{cancel}\newcommand{\abs}[1]{\left\lvert#1\right\rvert}
\newcommand{\point}[2]{\left(#1,#2\right)}
\definecolor{sapphire}{RGB}{59,90,125}
\definecolor{lightsapphire}{RGB}{110,154,187}
\definecolor{emerald}{RGB}{20,97,75}
\definecolor{lightemerald}{RGB}{18,168,131}
\newcommand{\highlight}[1]{\mathchoice{\colorbox{lightsapphire}{$\displaystyle #1$}}{\colorbox{lightsapphire}{$\textstyle #1$}}{\colorbox{lightsapphire}{$\scriptstyle #1$}}{\colorbox{lightsapphire}{$\scriptscriptstyle #1$}}}
\newcommand{\firsthighlight}[1]{\mathchoice{\colorbox{lightsapphire}{$\displaystyle #1$}}{\colorbox{lightsapphire}{$\textstyle #1$}}{\colorbox{lightsapphire}{$\scriptstyle #1$}}{\colorbox{lightsapphire}{$\scriptscriptstyle #1$}}}
\newcommand{\secondhighlight}[1]{\mathchoice{\colorbox{lightemerald}{$\displaystyle #1$}}{\colorbox{lightemerald}{$\textstyle #1$}}{\colorbox{lightemerald}{$\scriptstyle #1$}}{\colorbox{lightemerald}{$\scriptscriptstyle #1$}}}
\newcommand{\unhighlight}[1]{{\color{black}{{#1}}}}
\newcommand{\lowlight}[1]{{\color{lightgray}{#1}}}
\newcommand{\attention}[1]{\mathord{\overset{\downarrow}{#1}}}
\newcommand{\nextoperation}[1]{\mathord{\boxed{#1}}}
\newcommand{\substitute}[1]{{\color{blue}{{#1}}}}
\newcommand{\pinover}[2]{\overset{\overset{\mathrm{\ #2\ }}{|}}{\strut #1 \strut}}
\newcommand{\addright}[1]{{\color{blue}{{{}+#1}}}}
\newcommand{\addleft}[1]{{\color{blue}{{#1+{}}}}}
\newcommand{\subtractright}[1]{{\color{blue}{{{}-#1}}}}
\newcommand{\multiplyright}[2][\cdot]{{\color{blue}{{{}#1#2}}}}
\newcommand{\multiplyleft}[2][\cdot]{{\color{blue}{{#2#1{}}}}}
\newcommand{\divideunder}[2]{\frac{#1}{{\color{blue}{{#2}}}}}
\newcommand{\divideright}[1]{{\color{blue}{{{}\div#1}}}}
\newcommand{\negate}[1]{{\color{blue}{{-}}}\left(#1\right)}
\newcommand{\cancelhighlight}[1]{{\color{sapphire}{{\cancel{#1}}}}}
\newcommand{\secondcancelhighlight}[1]{{\color{emerald}{{\bcancel{#1}}}}}
\newcommand{\thirdcancelhighlight}[1]{\definecolor{amethyst}{RGB}{112,72,91}{\color{amethyst}{{\xcancel{#1}}}}}
\newcommand{\confirm}[1]{\stackrel{\checkmark}{#1}}
\newcommand{\reject}[1]{\stackrel{\text{no}}{#1}}
\newcommand{\wonder}[1]{\stackrel{\text{?}}{#1}}
\newcommand{\apple}{\text{🍎}}
\newcommand{\banana}{\text{🍌}}
\newcommand{\pear}{\text{🍐}}
\newcommand{\cat}{\text{🐱}}
\newcommand{\dog}{\text{🐶}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\newcommand{\sfrac}[2]{{#1}/{#2}}
\)
Appendix C Answers to Exercises
I Linear Equations and Lines
1 Variables, Expressions, Equations, and Inequalities
1.1 Variables and Evaluating Expressions
1.1.6 Exercises
Skills Practice
1.1.6.1.
1.1.6.1.a
Answer 1.
\(d\hbox{, }D\hbox{, }x\hbox{, or }y\)
Answer 2.
1.1.6.1.b
Answer 1.
\(w\hbox{, }W\hbox{, }x\hbox{, or }y\)
Answer 2.
1.1.6.3.
1.1.6.5.
1.1.6.7.
1.1.6.9.
1.1.6.11.
1.1.6.13.
1.1.6.15.
1.1.6.17.
1.1.6.17.a1.1.6.17.b1.1.6.19.
1.1.6.19.a1.1.6.19.b1.1.6.21.
1.1.6.21.a1.1.6.21.b1.1.6.23.
1.1.6.23.a1.1.6.23.b1.1.6.25.
1.1.6.27.
1.1.6.29.
1.1.6.31.
1.1.6.33.
1.1.6.35.
1.1.6.37.
1.1.6.39.
1.1.6.41.
1.1.6.43.
1.1.6.45.
1.1.6.47.
1.1.6.49.
1.1.6.51.
1.1.6.53.
1.1.6.55.
Applications
1.1.6.75.
Answer.
\(3.12019\ {\rm seconds}\)
1.1.6.81.
1.1.6.81.a1.1.6.81.b1.1.6.83.
1.1.6.85.
1.1.6.87.
1.1.6.89.
1.2 Combining Like Terms
1.2.5 Exercises
Prerequisite/Review Skills
1.2.5.1.
1.2.5.3.
1.2.5.5.
1.2.5.7.
1.2.5.9.
1.2.5.11.
1.2.5.13.
1.2.5.15.
1.2.5.17.
1.2.5.19.
1.2.5.21.
1.2.5.23.
1.2.5.25.
1.2.5.27.
1.2.5.29.
1.2.5.31.
Skills Practice
1.2.5.33.
1.2.5.35.
Answer.
\(-53i, 26c, -{\frac{1}{2}}c, 35i\)
1.2.5.37.
Answer.
\(1y^{8}, -2.8y^{1}, -1y^{0}\)
1.2.5.39.
Answer.
\(9.9t^{7}, -{\frac{1}{9}}t^{5}, -1t^{7}\)
1.2.5.41.
1.2.5.43.
1.2.5.45.
1.2.5.47.
Answer.
\(-5n-n^{4}+\frac{5}{2}n^{5}\)
1.2.5.49.
Answer.
\(\frac{1}{3}z+\frac{-19}{20}q\)
1.2.5.51.
1.2.5.53.
1.2.5.55.
1.2.5.57.
1.2.5.59.
1.2.5.61.
Answer.
\(\frac{53}{45}R+\frac{5}{4}g\)
1.2.5.63.
1.2.5.65.
1.2.5.67.
Answer.
\(\frac{-24}{7}z^{5}+\frac{29}{30}z^{6}\)
Applications
1.2.5.69.
Answer.
\(\frac{5}{3}K+\frac{64}{15}s\)
1.2.5.71.
1.2.5.73.
Answer.
\(\frac{27}{20}h+\frac{9}{14}Y+\frac{7}{6}T\)
1.2.5.75. Office Lunch.
1.2.5.75.a1.2.5.75.b
1.2.5.77. Sportsball.
1.2.5.77.a1.2.5.77.b
1.3 Comparison Symbols and Notation for Intervals
1.3.4 Exercises
Prerequisite/Review Skills
1.3.4.1.
1.3.4.3.
1.3.4.5.
1.3.4.7.
1.3.4.9.
1.3.4.11.
1.3.4.13.
1.3.4.15.
Skills Practice
1.3.4.17.
1.3.4.19.
1.3.4.21.
1.3.4.23.
1.3.4.25.
1.3.4.27.
1.3.4.29.
1.3.4.31.
1.3.4.33.
1.3.4.35.
1.3.4.37.
1.3.4.39.
1.3.4.41.
Answer.
\({\frac{11}{7}}>{\frac{4}{3}}>{\frac{4}{9}}>{\frac{1}{6}}>{\frac{1}{8}}\)
1.3.4.43.
Answer.
\({\frac{9}{14}}>{\frac{5}{9}}>\sqrt{5}>9.1>\frac{\pi }{4}\)
1.3.4.45.
Answer 1.
\(\left\{x \mid x < -5\right\}\)
Answer 2.
\(\left(-\infty ,-5\right)\)
1.3.4.47.
Answer 1.
\(\left\{x \mid x\le -2\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
1.3.4.49.
Answer 1.
\(\left\{x \mid x\ge 1\right\}\)
Answer 2.
\(\left[1,\infty \right)\)
1.3.4.51.
Answer 1.
\(\left\{x \mid x > 4\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
1.3.4.53.
Answer 1.
\(\left\{\text{interval}, \left[-7,\infty \right)\right\}\)
Answer 2.
\(\left[-7,\infty \right)\)
1.3.4.55.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right)\right\}\)
Answer 2.
\(\left(-\infty ,-4\right)\)
1.3.4.57.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-1\right]\right\}\)
Answer 2.
\(\left(-\infty ,-1\right]\)
1.3.4.59.
Answer 1.
\(\left\{\text{interval}, \left(3,\infty \right)\right\}\)
Answer 2.
\(\left(3,\infty \right)\)
1.3.4.61.
Answer 1.
\(\left\{\text{interval}, \left[6,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x\ge 6\right\}\)
1.3.4.63.
Answer 1.
\(\left\{\text{interval}, \left(-6,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x > -6\right\}\)
1.3.4.65.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left\{x \mid x < -2\right\}\)
1.3.4.67.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left\{x \mid x\le 1\right\}\)
Applications
1.3.4.69.
Answer 1.
\(\left\{a \mid a\ge 21\right\}\)
Answer 2.
\(\left[21,\infty \right)\)
1.3.4.71.
Answer 1.
\(\left\{d \mid d\ge 5000\right\}\)
Answer 2.
\(\left[5000,\infty \right)\)
1.3.4.73.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Challenge
1.3.4.75.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
1.4 Equations, Inequalities, and Solutions
1.4.6 Exercises
Prerequisite/Review Skills
Skills Practice
1.4.6.9.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.11.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.13.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.15.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.17.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.19.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.21.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.23.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.25.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.27.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.29.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.31.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.33.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.35.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.37.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.39.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.41.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.43.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.45.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.47.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.49.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.51.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.53.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.55.
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.57.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.59.
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.61.
Answer.
\(\text{Choice 2, Choice 3, Choice 4}\)
1.4.6.63.
Answer.
\(\text{Choice 1, Choice 2}\)
1.4.6.65.
Answer.
\(\text{Choice 5, Choice 6}\)
Applications
1.4.6.67.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.69.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.71.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.73.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.75.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.5 Solving One-Step Equations
1.5.6 Exercises
Review and Warmup
1.5.6.1.
1.5.6.3.
1.5.6.5.
1.5.6.7.
1.5.6.9.
1.5.6.11.
1.5.6.13.
1.5.6.15.
1.5.6.17.
1.5.6.19.
1.5.6.21.
Skills Practice
1.5.6.23.
1.5.6.25.
1.5.6.27.
1.5.6.29.
1.5.6.31.
1.5.6.33.
Answer.
\(\left\{\frac{-17}{11}\right\}\)
1.5.6.35.
1.5.6.37.
1.5.6.39.
Answer.
\(\left\{\frac{-25}{28}\right\}\)
1.5.6.41.
Answer.
\(\left\{\frac{-35}{6}\right\}\)
1.5.6.43.
Answer.
\(\left\{\frac{3}{4}\right\}\)
1.5.6.45.
Answer.
\(\left\{\frac{12}{35}\right\}\)
1.5.6.47.
Answer.
\(\left\{\frac{-9}{4}\right\}\)
1.5.6.49.
1.5.6.51.
1.5.6.53.
Answer.
\(\left\{-26.47\right\}\)
1.5.6.55.
1.5.6.57.
1.5.6.59.
Answer.
\(\left\{-1.50704\right\}\)
Applications
1.5.6.69.
Answer 1.
Answer 2.
\(78.8\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)
Challenge
1.5.6.71.
1.6 Solving One-Step Inequalities
1.6.4 Exercises
Skills Practice
1.6.4.1.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
Answer 3.
\(\left\{n \mid n > 4\right\}\)
1.6.4.3.
Answer 1.
\(\left\{\text{interval}, \left[-5,\infty \right)\right\}\)
Answer 2.
\(\left[-5,\infty \right)\)
Answer 3.
\(\left\{z \mid z\ge -5\right\}\)
1.6.4.5.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-1\right)\right\}\)
Answer 2.
\(\left(-\infty ,-1\right)\)
Answer 3.
\(\left\{K \mid K < -1\right\}\)
1.6.4.7.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right]\right\}\)
Answer 2.
\(\left(-\infty ,3\right]\)
Answer 3.
\(\left\{X \mid X\le 3\right\}\)
1.6.4.9.
Answer 1.
\(\left\{\text{interval}, \left(-4,\infty \right)\right\}\)
Answer 2.
\(\left(-4,\infty \right)\)
Answer 3.
\(\left\{i \mid i > -4\right\}\)
1.6.4.11.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,6\right)\right\}\)
Answer 2.
\(\left(-\infty ,6\right)\)
Answer 3.
\(\left\{u \mid u < 6\right\}\)
1.6.4.13.
Answer 1.
\(\left\{\text{interval}, \left(2,\infty \right)\right\}\)
Answer 2.
\(\left(2,\infty \right)\)
Answer 3.
\(\left\{E \mid E > 2\right\}\)
1.6.4.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right]\right\}\)
Answer 2.
\(\left(-\infty ,5\right]\)
Answer 3.
\(\left\{Q \mid Q\le 5\right\}\)
1.6.4.17.
Answer 1.
\(\left\{\text{interval}, \left[-4,\infty \right)\right\}\)
Answer 2.
\(\left[-4,\infty \right)\)
Answer 3.
\(\left\{c \mid c\ge -4\right\}\)
1.6.4.19.
Answer 1.
\(\left\{\text{interval}, \left[-2,\infty \right)\right\}\)
Answer 2.
\(\left[-2,\infty \right)\)
Answer 3.
\(\left\{n \mid n\ge -2\right\}\)
1.7 Algebraic Properties and Simplifying Expressions
1.7.6 Exercises
Vocabulary
1.7.6.1.
1.7.6.3.
1.7.6.5.
1.7.6.7.
1.7.6.9.
1.7.6.11.
Skills Practice
1.7.6.13.
1.7.6.15.
Answer.
\(\left({\frac{6}{5}}+z^{2}\right)+z\)
1.7.6.17.
Answer.
\(15\mathopen{}\left(JT\right)\)
1.7.6.19.
1.7.6.21.
1.7.6.23.
1.7.6.25.
Answer.
\(\left(E+3\right)\cdot 2\)
1.7.6.27.
Answer.
\(5\mathopen{}\left(9+Q\right)\)
1.7.6.29.
1.7.6.31.
1.7.6.33.
Answer.
\(\frac{5}{2}y+\frac{5}{2}\frac{5}{4}\)
1.7.6.35.
Answer.
\(-J-\left(\frac{7}{6}\right)\)
1.7.6.37.
1.7.6.39.
1.7.6.41.
1.7.6.43.
1.7.6.45.
1.7.6.47.
1.7.6.49.
1.7.6.51.
1.7.6.53.
1.7.6.55.
1.7.6.57.
Answer.
\(\frac{249}{5}t+\frac{-81}{7}\)
1.7.6.59.
Critical Thinking
1.7.6.61.
1.7.6.61.a1.7.6.61.b
1.8 Modeling with Equations and Inequalities
1.8.6 Exercises
Review and Warmup
1.8.6.1.
1.8.6.1.a
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
1.8.6.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{years or months}}\)
1.8.6.1.c
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{hours or minutes}}\)
Skills Practice
1.8.6.3.
1.8.6.5.
1.8.6.7.
1.8.6.9.
1.8.6.11.
1.8.6.13.
Answer.
\(13\mathopen{}\left(x+10\right)\)
1.8.6.15.
1.8.6.17.
1.8.6.19.
1.8.6.21.
1.8.6.23.
1.8.6.25.
1.8.6.27.
1.8.6.29.
1.8.6.31.
1.8.6.33.
1.8.6.35.
Answer.
\(5\mathopen{}\left(x+15\right) = 9\)
1.8.6.37.
Applications
1.8.6.39.
1.8.6.41.
1.8.6.43.
1.8.6.45.
1.8.6.47.
1.8.6.49.
1.8.6.51.
1.8.6.53.
1.8.6.55.
1.8.6.57.
1.8.6.59.
1.8.6.61.
1.8.6.63.
1.8.6.65.
1.8.6.67.
1.8.6.69.
1.8.6.71.
Challenge
1.8.6.73.
1.9 Variables, Expressions, and Equations Chapter Review
Review Exercises for Chapter 1
Section 1: Variables and Evaluating Expressions
1.9.1.
1.9.1.a
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{hours or minutes}}\)
1.9.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }s\hbox{, }S\hbox{, }x\hbox{, or }y\)
Answer 2.
1.9.3.
1.9.5.
1.9.5.a1.9.5.b1.9.7.
1.9.9.
1.9.11.
1.9.13.
1.9.15.
1.9.17.
Section 2: Combining Like Terms
1.9.23.
Answer.
\(\frac{29}{12}w+\frac{13}{10}Z\)
Section 3: Comparison Symbols and Notation for Intervals
1.9.25.
1.9.29.
Answer 1.
\(\left\{x \mid x\le -6\right\}\)
Answer 2.
\(\left(-\infty ,-6\right]\)
1.9.31.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-3\right)\right\}\)
Answer 2.
\(\left\{x \mid x < -3\right\}\)
1.9.33.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Section 4: Equations, Inequalities, and Solutions
1.9.35.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.37.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.9.39.
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.41.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.9.43.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
1.9.45.
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Section 5: Solving One-Step Equations
1.9.51.
Section 6: Solving One-Step Inequalities
1.9.53.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
Answer 3.
\(\left\{L \mid L\le 1\right\}\)
Section 7: Algebraic Properties and Simplifying Expressions
1.9.55.
1.9.57.
Answer.
\(\left(j+2\right)\cdot 3\)
Section 8: Modeling with Equations and Inequalities
1.9.63.
1.9.63.a
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
1.9.63.b
Answer 1.
\(d\hbox{, }D\hbox{, }m\hbox{, }M\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
1.9.63.c
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
Applications
1.9.69.
1.9.71.
Answer.
\(327500+165000t = 1.31\times 10^{6}\)
1.9.73.
1.9.75.
2 Linear Equations and Inequalities
2.1 Solving Multistep Linear Equations
2.1.6 Exercises
Review and Warmup
2.1.6.1.
2.1.6.3.
2.1.6.5.
Answer.
\(\left\{\frac{-7}{10}\right\}\)
Vocabulary
2.1.6.7.
2.1.6.7.a2.1.6.7.b2.1.6.7.c2.1.6.7.dSkills Practice
2.1.6.9.
2.1.6.11.
2.1.6.13.
2.1.6.15.
Answer.
\(\left\{\frac{7}{5}\right\}\)
2.1.6.17.
Answer.
\(\left\{\frac{14}{5}\right\}\)
2.1.6.19.
Answer.
\(\left\{\frac{-4}{9}\right\}\)
2.1.6.21.
Answer.
\(\left\{-0.263158\right\}\)
2.1.6.23.
Answer.
\(\left\{-1.58696\right\}\)
2.1.6.25.
Answer.
\(\left\{2.17647\right\}\)
2.1.6.27.
2.1.6.29.
2.1.6.31.
2.1.6.33.
2.1.6.35.
2.1.6.37.
2.1.6.39.
Answer.
\(\left\{\frac{-10}{3}\right\}\)
2.1.6.41.
Answer.
\(\left\{\frac{17}{4}\right\}\)
2.1.6.43.
Answer.
\(\left\{\frac{14}{11}\right\}\)
2.1.6.45.
Answer.
\(\left\{\frac{-1}{9}\right\}\)
2.1.6.47.
2.1.6.49.
2.1.6.51.
Answer.
\(\left\{\frac{4}{3}\right\}\)
Applications
2.1.6.53.
2.1.6.55.
2.1.6.57.
2.1.6.59.
2.1.6.61.
2.1.6.63.
2.1.6.65.
2.1.6.67.
2.1.6.69.
2.1.6.71.
2.2 Solving Multistep Linear Inequalities
2.2.4 Exercises
Review and Warmup
2.2.4.1.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right)\right\}\)
Answer 2.
\(\left(-\infty ,3\right)\)
Answer 3.
\(\left\{h \mid h < 3\right\}\)
2.2.4.3.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,4\right]\right\}\)
Answer 2.
\(\left(-\infty ,4\right]\)
Answer 3.
\(\left\{t \mid t\le 4\right\}\)
Skills Practice
2.2.4.5.
Answer 1.
\(\left\{\text{interval}, \left[-2,\infty \right)\right\}\)
Answer 2.
\(\left[-2,\infty \right)\)
Answer 3.
\(\left\{D \mid D\ge -2\right\}\)
2.2.4.7.
Answer 1.
\(\left\{\text{interval}, \left[2,\infty \right)\right\}\)
Answer 2.
\(\left[2,\infty \right)\)
Answer 3.
\(\left\{P \mid P\ge 2\right\}\)
2.2.4.9.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,6\right]\right\}\)
Answer 2.
\(\left(-\infty ,6\right]\)
Answer 3.
\(\left\{b \mid b\le 6\right\}\)
2.2.4.11.
Answer 1.
\(\left\{\text{interval}, \left[-3,\infty \right)\right\}\)
Answer 2.
\(\left[-3,\infty \right)\)
Answer 3.
\(\left\{m \mid m\ge -3\right\}\)
2.2.4.13.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right)\right\}\)
Answer 2.
\(\left(-\infty ,1\right)\)
Answer 3.
\(\left\{y \mid y < 1\right\}\)
2.2.4.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right)\right\}\)
Answer 2.
\(\left(-\infty ,5\right)\)
Answer 3.
\(\left\{J \mid J < 5\right\}\)
2.2.4.17.
Answer 1.
\(\left\{\text{interval}, \left(-4,\infty \right)\right\}\)
Answer 2.
\(\left(-4,\infty \right)\)
Answer 3.
\(\left\{W \mid W > -4\right\}\)
2.2.4.19.
Answer 1.
\(\left\{\text{interval}, \left(5,\infty \right)\right\}\)
Answer 2.
\(\left(5,\infty \right)\)
Answer 3.
\(\left\{g \mid g > 5\right\}\)
2.2.4.21.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
Answer 3.
\(\left\{s \mid s > 4\right\}\)
2.2.4.23.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-5\right)\right\}\)
Answer 2.
\(\left(-\infty ,-5\right)\)
Answer 3.
\(\left\{D \mid D < -5\right\}\)
2.2.4.25.
Answer 1.
\(\left\{\text{interval}, \left(-1,\infty \right)\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 3.
\(\left\{P \mid P > -1\right\}\)
2.2.4.27.
Answer 1.
\(\left\{\text{interval}, \left(3,\infty \right)\right\}\)
Answer 2.
\(\left(3,\infty \right)\)
Answer 3.
\(\left\{b \mid b > 3\right\}\)
2.2.4.29.
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
Answer 3.
\(\left\{m \mid m\ge -6\right\}\)
2.2.4.31.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left(-\infty ,-2\right)\)
Answer 3.
\(\left\{x \mid x < -2\right\}\)
Applications
2.2.4.33.
2.2.4.33.a2.2.4.33.b2.2.4.33.c2.2.4.35.
2.2.4.35.a2.2.4.35.b2.2.4.35.cAnswer.
\(\left[5.1,\infty \right)\)
2.2.4.37.
2.2.4.37.a2.2.4.37.b2.2.4.37.cAnswer.
\(\left[10000,80834\right)\)
2.3 Equations and Inequalities with Fractions
2.3.5 Exercises
Review and Warmup
2.3.5.1.
2.3.5.3.
2.3.5.5.
Skills Practice
2.3.5.7.
Answer 1.
Answer 2.
\(\left\{\frac{1}{21}\right\}\)
2.3.5.9.
Answer 1.
Answer 2.
\(\left\{\frac{-53}{99}\right\}\)
2.3.5.11.
Answer 1.
Answer 2.
\(\left\{\frac{141}{7}\right\}\)
2.3.5.13.
Answer 1.
Answer 2.
\(\left\{\frac{-15}{16}\right\}\)
2.3.5.15.
Answer 1.
Answer 2.
\(\left\{\frac{282}{35}\right\}\)
2.3.5.17.
Answer 1.
Answer 2.
\(\left\{\frac{19}{25}\right\}\)
2.3.5.19.
Answer 1.
Answer 2.
\(\left\{\frac{19}{21}\right\}\)
2.3.5.21.
Answer 1.
Answer 2.
\(\left\{\frac{50}{3}\right\}\)
2.3.5.23.
2.3.5.25.
Answer 1.
Answer 2.
\(\left\{\frac{-29}{35}\right\}\)
2.3.5.27.
Answer 1.
Answer 2.
\(\left\{x \mid x\ge \frac{-1}{6}\right\}\)
Answer 3.
\(\left[-{\frac{1}{6}},\infty \right)\)
2.3.5.29.
Answer 1.
Answer 2.
\(\left\{x \mid x\le \frac{-9}{5}\right\}\)
Answer 3.
\(\left(-\infty ,-{\frac{9}{5}}\right]\)
2.3.5.31.
Answer 1.
Answer 2.
\(\left\{x \mid x\ge \frac{-116}{5}\right\}\)
Answer 3.
\(\left[-{\frac{116}{5}},\infty \right)\)
2.3.5.33.
Answer 1.
Answer 2.
\(\left\{x \mid x\le \frac{-23}{27}\right\}\)
Answer 3.
\(\left(-\infty ,-{\frac{23}{27}}\right]\)
2.3.5.35.
Answer 1.
Answer 2.
\(\left\{x \mid x < \frac{628}{345}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{628}{345}}\right)\)
Applications
2.3.5.37.
2.3.5.39.
2.3.5.41.
2.3.5.43.
2.3.5.45.
2.3.5.47.
Challenge
2.3.5.49.
2.4 Special Solution Sets
2.4.4 Exercises
Notation
2.4.4.1.
Answer.
\(\text{no real solutions}\)
Skills Practice
2.4.4.3.
Answer.
\(\text{no real solutions}\)
2.4.4.5.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.7.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.9.
Answer.
\(\text{no real solutions}\)
2.4.4.11.
Answer.
\(\text{no real solutions}\)
2.4.4.13.
Answer.
\(\text{no real solutions}\)
2.4.4.15.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.17.
Answer.
\(\text{no real solutions}\)
2.4.4.19.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.21.
Answer.
\(\text{no real solutions}\)
2.4.4.23.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.25.
Answer.
\(\text{no real solutions}\)
2.4.4.27.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.29.
Answer.
\(\text{no real solutions}\)
2.4.4.31.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.33.
Answer.
\(\text{no real solutions}\)
2.4.4.35.
Answer.
\(\text{no real solutions}\)
2.4.4.37.
Answer.
\(\text{no real solutions}\)
2.4.4.39.
Answer.
\(\text{no real solutions}\)
Challenge
2.4.4.41.
Answer 1.
Answer 2.
\(20\mathopen{}\left(x+4\right)\)
2.5 Isolating a Linear Variable
2.5.3 Exercises
Skills Practice
2.5.3.1.
2.5.3.3.
2.5.3.5.
2.5.3.7.
2.5.3.9.
2.5.3.11.
2.5.3.13.
2.5.3.15.
2.5.3.17.
2.5.3.19.
2.5.3.21.
2.5.3.23.
2.5.3.25.
Answer.
\(y = {\frac{1}{4}}x+-{\frac{11}{8}}\)
2.6 Linear Equations and Inequalities Chapter Review
Review Exercises for Chapter 2
Section 1: Solving Multistep Linear Equations
2.6.1.
2.6.1.a2.6.1.b2.6.1.c2.6.1.d2.6.3.
2.6.5.
2.6.7.
Answer.
\(\left\{\frac{-39}{14}\right\}\)
2.6.9.
Answer.
\({\frac{84}{11}}\ {\rm yr}\)
2.6.11.
2.6.13.
3 Graphing Lines
3.1 Cartesian Coordinates
Exercises
3.1.1.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
3.1.3.
3.1.5.
3.1.7.
3.1.9.
3.1.11.
3.1.13.
Answer 1.
Answer 2.
Answer 3.
\(\left(2008,5\right), \left(2010,19\right), \left(2012,51\right)\)
3.1.15.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
3.1.17.
Answer 1.
Answer 2.
Answer 3.
3.1.19.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.2 Graphing Equations
Exercises
3.2.9.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.2.11.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.2.13.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.2.15.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.2.17.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.2.19.
Answer.
\(-1;\,14;\,0;\,0;\,1;\,-14;\,2;\,-28;\,3;\,-42\)
3.2.21.
Answer.
\(-1;\,5;\,0;\,2;\,1;\,-1;\,2;\,-4;\,3;\,-7\)
3.2.23.
Answer.
\(-6;\,-17;\,0;\,2;\,6;\,21;\,12;\,40;\,18;\,59\)
3.2.25.
Answer.
\(-8;\,18;\,0;\,7;\,8;\,-4;\,16;\,-15;\,24;\,-26\)
3.2.27.
Answer.
| \(x\) |
\(y\) |
Point |
| \(0\) |
\(900\) |
\((0,900)\) |
| \(1\) |
\(931\) |
\((1,931)\) |
| \(6\) |
\(1086\) |
\((6,1086)\) |
| \(12\) |
\(1272\) |
\((12,1272)\) |
| \(24\) |
\(1644\) |
\((24,1644)\) |
3.2.29.
Answer.
| \(T\) |
\(P\) |
Point |
| \(20\) |
\(\approx94.16\) |
\((20,94.16)\) |
| \(40\) |
\(\approx98.09\) |
\((40,98.09)\) |
| \(60\) |
\(\approx102.0\) |
\((60,102.0)\) |
| \(80\) |
\(\approx105.9\) |
\((80,105.9)\) |
| \(100\) |
\(\approx109.9\) |
\((100,109.9)\) |
3.2.31.
Answer.
| \(x\) |
\(y=2x+3\) |
Point |
| \(-2\) |
\(-1\) |
\((-2,-1)\) |
| \(-1\) |
\(1\) |
\((-1,1)\) |
| \(0\) |
\(3\) |
\((0,3)\) |
| \(1\) |
\(5\) |
\((1,5)\) |
| \(2\) |
\(7\) |
\((2,7)\) |
3.2.33.
Answer.
| \(x\) |
\(y=-4x+1\) |
Point |
| \(-2\) |
\(9\) |
\((-2,9)\) |
| \(-1\) |
\(5\) |
\((-1,5)\) |
| \(0\) |
\(1\) |
\((0,1)\) |
| \(1\) |
\(-3\) |
\((1,-3)\) |
| \(2\) |
\(-7\) |
\((2,-7)\) |
3.2.35.
Answer.
| \(x\) |
\(y=\frac{5}{2}x\) |
Point |
| \(-2\) |
\(-5\) |
\((-2,-5)\) |
| \(-1\) |
\(-\frac{5}{2}\) |
\((-1,-\frac{5}{2})\) |
| \(0\) |
\(0\) |
\((0,0)\) |
| \(1\) |
\(\frac{5}{2}\) |
\((1,\frac{5}{2})\) |
| \(2\) |
\(5\) |
\((2,5)\) |
3.2.37.
Answer.
| \(x\) |
\(y=-\frac{2}{5}x-3\) |
Point |
| \(-5\) |
\(-1\) |
\((-5,-1)\) |
| \(0\) |
\(-3\) |
\((0,-3)\) |
| \(5\) |
\(-5\) |
\((5,-5)\) |
3.2.39.
Answer.
| \(x\) |
\(y=x^2+1\) |
Point |
| \(-2\) |
\(5\) |
\((-2,5)\) |
| \(-1\) |
\(2\) |
\((-1,2)\) |
| \(0\) |
\(1\) |
\((0,1)\) |
| \(1\) |
\(2\) |
\((1,2)\) |
| \(2\) |
\(5\) |
\((2,5)\) |
3.2.41.
Answer.
| \(x\) |
\(y=-3x^2\) |
Point |
| \(-2\) |
\(-12\) |
\((-2,-12)\) |
| \(-1\) |
\(-3\) |
\((-1,3)\) |
| \(0\) |
\(0\) |
\((0,0)\) |
| \(1\) |
\(-3\) |
\((1,-3)\) |
| \(2\) |
\(-12\) |
\((2,-12)\) |
3.3 Exploring Two-Variable Data and Rate of Change
3.3.5 Exercises
3.3.5.1.
3.3.5.3.
3.3.5.5.
3.3.5.7.
3.3.5.9.
3.3.5.11.
3.3.5.13.
3.3.5.15.
3.3.5.17.
3.3.5.19.
3.3.5.21.
3.3.5.23.
3.3.5.25.
Answer 1.
\(2198.33\ {\textstyle\frac{\rm\mathstrut people}{\rm\mathstrut yr}}\)
Answer 2.
\(3905.71\ {\textstyle\frac{\rm\mathstrut people}{\rm\mathstrut yr}}\)
Answer 3.
3.4 Slope
3.4.5 Exercises
Review and Warmup
3.4.5.1.
3.4.5.3.
3.4.5.5.
3.4.5.7.
3.4.5.9.
Skills Practice
3.4.5.11.
3.4.5.13.
3.4.5.15.
3.4.5.17.
3.4.5.19.
3.4.5.21.
3.4.5.23.
3.4.5.25.
3.4.5.27.
Answer.
\(\text{DNE}\hbox{ or }\text{NONE}\)
3.4.5.29.
3.4.5.31.
3.4.5.33.
3.4.5.35.
3.4.5.37.
3.4.5.39.
Answer.
\(\text{DNE}\hbox{ or }\text{NONE}\)
3.4.5.41.
3.4.5.43.
Slope in Context
3.4.5.45.
3.4.5.47.
3.4.5.49.
Answer.
\(0.19\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut mo}}\)
3.4.5.51.
Answer.
\(3.6\ {\textstyle\frac{\rm\mathstrut g}{\rm\mathstrut min}}\)
3.4.5.53.
Answer 1.
\(375\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 2.
\(125\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 3.
\(0\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 4.
\(-500\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
3.4.5.55.
Answer.
\(244.064\ {\textstyle\frac{\rm\mathstrut diagnoses}{\rm\mathstrut yr}}\)
Challenge
3.4.5.57.
3.5 Slope-Intercept Form
3.5.7 Exercises
Review and Warmup
Skills Practice
3.5.7.5.
3.5.7.7.
3.5.7.9.
3.5.7.11.
3.5.7.13.
3.5.7.15.
3.5.7.17.
3.5.7.19.
3.5.7.21.
3.5.7.23.
3.5.7.25.
3.5.7.27.
3.5.7.29.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}\)
3.5.7.31.
3.5.7.33.
3.5.7.35.
3.5.7.37.
3.5.7.39.
3.5.7.41.
3.5.7.43.
3.5.7.45.
3.5.7.47.
3.5.7.49.
3.5.7.51.
3.5.7.53.
3.5.7.55.
3.5.7.57.
Applications
3.5.7.59.
3.5.7.61.
3.5.7.63.
3.5.7.65.
Answer 1.
Answer 2.
Answer 3.
3.5.7.67.
Answer 1.
Answer 2.
Answer 3.
3.5.7.69.
Answer 1.
Answer 2.
Answer 3.
3.5.7.71.
Answer 1.
Answer 2.
Answer 3.
3.6 Point-Slope Form
3.6.5 Exercises
Review and Warmup
Skills Practice
3.6.5.5.
3.6.5.7.
3.6.5.9.
3.6.5.11.
3.6.5.13.
Answer 1.
\(y = 5\mathopen{}\left(x-3\right)+16\)
Answer 2.
\(y = 5\mathopen{}\left(x-2\right)+11\)
3.6.5.15.
Answer 1.
\(y = -2\mathopen{}\left(x--2\right)+8\)
Answer 2.
\(y = -2\mathopen{}\left(x-3\right)+-2\)
3.6.5.17.
Answer 1.
\(y = \frac{4}{7}\mathopen{}\left(x+14\right)+-16\)
Answer 2.
\(y = \frac{4}{7}\mathopen{}\left(x-7\right)+-4\)
3.6.5.19.
Answer 1.
\(y = 4\mathopen{}\left(x-5\right)+25\)
Answer 2.
3.6.5.21.
Answer 1.
\(y = -2\mathopen{}\left(x-3\right)+-8\)
Answer 2.
3.6.5.23.
Answer 1.
\(y = 1\mathopen{}\left(x-1\right)+-3\)
Answer 2.
3.6.5.25.
Answer 1.
\(y = -1\mathopen{}\left(x-5\right)+-7\)
Answer 2.
3.6.5.27.
Answer 1.
\(y = {\frac{5}{3}}\mathopen{}\left(x--9\right)+-17\)
Answer 2.
\(y = {\frac{5}{3}}x+-2\)
3.6.5.29.
Answer 1.
\(y = -{\frac{7}{6}}\mathopen{}\left(x-18\right)+-25\)
Answer 2.
\(y = -{\frac{7}{6}}x+-4\)
3.6.5.31.
3.6.5.33.
3.6.5.35.
3.6.5.37.
3.6.5.39.
Answer.
\(y = {\frac{3}{4}}\mathopen{}\left(x-5\right)+5\)
3.6.5.41.
Answer.
\(y = -{\frac{3}{2}}\mathopen{}\left(x-1\right)-4\)
3.6.5.43.
Answer.
\(y = {\frac{200}{3}}\mathopen{}\left(x+1\right)-500\)
3.6.5.45.
Answer.
\(y = -{\frac{200}{3}}\mathopen{}\left(x-2\right)+500\)
3.6.5.47.
Answer.
\(y = {\frac{29}{72}}\mathopen{}\left(x-1131\right)+397\hbox{ or }y = {\frac{29}{72}}\mathopen{}\left(x-627\right)+194\)
3.6.5.49.
Answer.
\(y = -{\frac{368}{593}}\mathopen{}\left(x-521\right)+369\hbox{ or }y = -{\frac{368}{593}}\mathopen{}\left(x-1114\right)+1\)
3.6.5.51.
3.6.5.53.
3.6.5.55.
3.6.5.57.
Applications
3.6.5.59.
Answer 1.
\(y = 0.04\mathopen{}\left(x-230\right)+27.2\)
Answer 2.
Answer 3.
3.6.5.61.
Answer 1.
\(y = 0.18\mathopen{}\left(x-10\right)+14.2\)
Answer 2.
Answer 3.
3.6.5.63.
Answer 1.
\(y = -39000\mathopen{}\left(x-4\right)+638000\hbox{ or }y = -39000\mathopen{}\left(x-7\right)+521000\)
Answer 2.
Answer 3.
3.6.5.65.
Answer 1.
\(y = -8.1\mathopen{}\left(x-9\right)+324\hbox{ or }y = -8.1\mathopen{}\left(x-12\right)+299.7\)
Answer 2.
Answer 3.
3.7 Standard Form
3.7.5 Exercises
Review and Warmup
3.7.5.1.
3.7.5.3.
3.7.5.5.
Answer.
\(y = {\frac{3}{8}}x+{\frac{9}{4}}\)
Skills Practice
3.7.5.7.
3.7.5.9.
3.7.5.11.
3.7.5.13.
3.7.5.15.
3.7.5.17.
Answer 1.
Answer 2.
\(\left(0,\frac{5}{12}\right)\)
3.7.5.23.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.7.5.25.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.7.5.27.
Answer.
\(x\)-intercept: \((6,0)\)
\(y\)-intercept: \((0,4)\)
3.7.5.29.
Answer.
\(x\)-intercept: \((2,0)\)
\(y\)-intercept: \((0,-5)\)
3.7.5.31.
Answer.
\(x\)-intercept: \((-15,0)\)
\(y\)-intercept: \((0,-3)\)
3.7.5.33.
3.7.5.35.
3.7.5.37.
3.7.5.39.
3.7.5.41.
3.7.5.43.
3.7.5.45.
3.7.5.47.
Challenge
3.7.5.49.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.8 Horizontal, Vertical, Parallel, and Perpendicular Lines
3.8.5 Exercises
Review and Warmup
3.8.5.1.
3.8.5.3.
3.8.5.5.
Answer.
\(\text{DNE}\hbox{ or }\text{NONE}\)
Skills Practice
3.8.5.11.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.8.5.13.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.8.5.23.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.8.5.25.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.8.5.31.
3.8.5.33.
3.8.5.35.
Answer.
\(\text{neither parallel nor perpendicular}\)
3.8.5.37.
3.8.5.39.
3.8.5.41.
3.8.5.43.
Answer 1.
\(y = 2\mathopen{}\left(x-5\right)+3\)
Answer 2.
3.8.5.45.
Answer 1.
\(y = -{\frac{9}{4}}\mathopen{}\left(x+3\right)+{\frac{47}{4}}\)
Answer 2.
\(y = -{\frac{9}{4}}x+5\)
3.8.5.47.
3.8.5.49.
Answer 1.
\(y = -{\frac{9}{5}}\mathopen{}\left(x-2\right)+-{\frac{43}{5}}\)
Answer 2.
\(y = -{\frac{9}{5}}x-5\)
3.9 Summary of Graphing Lines
3.9.5 Exercises
3.9.5.1.
Answer.
| \(x\) |
\(y\) |
| \(-2\) |
\(-5\) |
| \(-1\) |
\(-1\) |
| \(0\) |
\(3\) |
| \(1\) |
\(7\) |
| \(2\) |
\(11\) |
3.9.5.3.
Answer.
| \(x\) |
\(y\) |
| \(-8\) |
\(5\) |
| \(-4\) |
\(2\) |
| \(0\) |
\(-1\) |
| \(4\) |
\(-4\) |
| \(8\) |
\(-7\) |
3.9.5.5.
Answer.
\begin{align*}
x\text{-intercept:}~\amp(-15,0)\\
y\text{-intercept:}~\amp(0,-18)\\
\text{another point:}~\amp(-10,-6)
\end{align*}
3.9.5.7.
Answer.
\begin{align*}
x\text{-intercept:}~\amp(-3,0)\\
y\text{-intercept:}~\amp(0,-9)\\
\text{another point:}~\amp(1,-12)
\end{align*}
3.9.5.9.
Answer.
\begin{align*}
x\text{-intercept:}~\amp(-0.75,0)\\
y\text{-intercept:}~\amp(0,-1)\\
\text{another point:}~\amp(-3,3)
\end{align*}
3.9.5.11.
Answer.
\begin{align*}
x\text{-intercept:}~\amp(0,0)\\
y\text{-intercept:}~\amp(0,0)\\
\text{another point:}~\amp(3,5)
\end{align*}
3.9.5.21.
3.9.5.23.
3.9.5.25.
3.9.5.27.
3.9.5.29.
3.9.5.31.
3.9.5.33.
3.10 Graphing Lines Chapter Review
3.10.9 Exercises
3.10.9.7.
3.10.9.9.
3.10.9.11.
3.10.9.13.
3.10.9.15.
3.10.9.17.
Answer.
\(\text{DNE}\hbox{ or }\text{NONE}\)
3.10.9.19.
3.10.9.21.
3.10.9.23.
Answer 1.
\(y = \frac{1}{6}\mathopen{}\left(x-6\right)+4\)
Answer 2.
\(y = \frac{1}{6}\mathopen{}\left(x+6\right)+2\)
3.10.9.25.
Answer 1.
Answer 2.
Answer 3.
3.10.9.27.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
3.10.9.29.
3.10.9.31.
Answer 1.
Answer 2.
\(\left(0,\frac{3}{20}\right)\)
3.10.9.33.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 5.
Answer 6.
Answer 7.
Answer 8.
Answer 9.
Answer 10.
3.10.9.35.
3.10.9.37.
3.10.9.39.
Answer 1.
\(y = {\frac{9}{8}}\mathopen{}\left(x+3\right)+-{\frac{19}{8}}\)
Answer 2.
3.10.9.41.
3.10.9.43.
4 Systems of Two Linear Equations
4.1 Solving a System by Graphing
4.1.5 Exercises
Review
4.1.5.1.
Answer.
\(\text{Choice 2, Choice 3, Choice 4}\)
Skills Practice
4.1.5.3.
Answer.
\(\text{Yes, it is a solution.}\)
4.1.5.5.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.7.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.9.
4.1.5.11.
4.1.5.13.
4.1.5.15.
Answer 1.
Answer 2.
\(\text{None of the above}\)
4.1.5.17.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
4.1.5.19.
4.1.5.21.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(8,-11\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-6\right), \left(8,-19\right)\right\}\)
Answer 2.
4.1.5.23.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-4,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-9\right), \left(6,-10\right)\right\}\)
Answer 2.
4.1.5.25.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-9\right), \left(1,0\right)\right\}\)
Answer 2.
4.1.5.27.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,0\right), \left(0,-2\right)\right\}\)
Answer 2.
4.1.5.29.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(5,0\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, -13, \left(0,9\right)\right\}\)
Answer 2.
4.1.5.31.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-4,0\right), \left(0,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,3\right), \left(0,2\right)\right\}\)
Answer 2.
4.1.5.33.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-2,0\right), \left(0,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(9,5\right), \left(-4,-3\right)\right\}\)
Answer 2.
4.1.5.35.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(1,0\right), \left(0,-5\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.37.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,-8\right), \left(1,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,8\right), \left(7,19\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.39.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,8\right), \left(8,13\right)\right\}\)
Answer 2.
Applications
4.1.5.41.
4.1.5.41.a4.1.5.41.bAnswer.
\(\left\{\text{line}, \text{solid}, \left(0,90\right), \left(50,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,70\right), \left(70,0\right)\right\}\)
4.1.5.43.
4.1.5.43.a4.1.5.43.bAnswer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,65\right), \left(1,55\right)\right\}\)
4.2 Substitution
4.2.5 Exercises
Skills Practice
4.2.5.1.
4.2.5.3.
4.2.5.5.
4.2.5.7.
4.2.5.9.
4.2.5.11.
4.2.5.13.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.15.
4.2.5.17.
4.2.5.19.
4.2.5.21.
Answer.
\(f = -{\frac{3}{7}}, V = {\frac{11}{7}}\)
4.2.5.23.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.25.
Answer.
\(C = -{\frac{43}{8}}, z = {\frac{5}{4}}\)
4.2.5.27.
Answer.
\(N = -{\frac{1}{2}}, Q = -{\frac{5}{2}}\)
4.2.5.29.
Answer.
\(a = -{\frac{6}{5}}, h = -{\frac{7}{5}}\)
4.2.5.31.
Answer.
\(l = -{\frac{8}{5}}, w = 9\)
4.2.5.33.
Answer.
\(x = -2, L = {\frac{5}{2}}\)
4.2.5.35.
Answer.
\(H = 3.23077, c = -6.47692\)
4.2.5.37.
Answer.
\(T = 7.12813, r = -0.93125\)
4.2.5.39.
Answer.
\(f = 2, H = {\frac{7}{15}}\)
4.2.5.41.
Answer.
\(r = {\frac{1}{3}}, X = -{\frac{5}{18}}\)
4.2.5.43.
Answer.
\(C = {\frac{7}{36}}, m = {\frac{2}{3}}\)
4.2.5.45.
4.2.5.47.
Answer.
\(a = -{\frac{35}{47}}, S = -{\frac{32}{47}}\)
4.2.5.49.
Answer 1.
\(k = {\frac{12}{7}}, i = -{\frac{44}{7}}\)
Answer 2.
4.2.5.51.
Answer.
\(\text{infinitely many solutions}\)
Applications
4.2.5.53.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.2.5.55.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.2.5.57.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.2.5.59.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.2.5.61.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.3 Elimination
4.3.5 Exercises
Skills Practice
4.3.5.1.
4.3.5.3.
4.3.5.5.
4.3.5.7.
4.3.5.9.
4.3.5.11.
4.3.5.13.
Answer.
\(q = -{\frac{20}{9}}, x = 4\)
4.3.5.15.
Answer.
\(B = {\frac{1}{4}}, L = 2\)
4.3.5.17.
Answer.
\(M = 63.5, c = -238.333\)
4.3.5.19.
Answer.
\(Z = -{\frac{15}{2}}, r = {\frac{77}{8}}\)
4.3.5.21.
Answer.
\(\text{infinitely many solutions}\)
4.3.5.23.
4.3.5.25.
4.3.5.27.
4.3.5.29.
4.3.5.31.
Answer.
\(\text{infinitely many solutions}\)
Applications
4.3.5.33.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.3.5.35.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Challenge
4.3.5.37.
4.4 Systems of Two Linear Equations Chapter Review
Review Exercises for [cross-reference to target(s) "chapter-systems-of-linear-equations" missing or not unique]
Section 1: Solving a System by Graphing
4.4.1.
Answer.
\(\text{Yes, it is a solution.}\)
4.4.3.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
4.4.5.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(1,0\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-4\right), \left(3,6\right)\right\}\)
Answer 2.
4.4.7.
4.4.7.a4.4.7.bAnswer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,150\right), \left(1,138\right)\right\}\)
Section 2: Substitution
4.4.9.
4.4.11.
Answer.
\(\text{infinitely many solutions}\)
4.4.13.
Answer.
\(v = 4.85714, x = -35.1143\)
4.4.15.
Answer.
\(G = -{\frac{15}{16}}, M = -{\frac{3}{2}}\)
4.4.17.
Answer 1.
Answer 2.
Answer 3.
\(8.76923\ {\rm months}\)
Answer 4.
4.4.19.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Section 3: Elimination
4.4.25.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
