Chapter 2

Solve the absolute value equation. $$|x-3|=|8-x|$$

Solve the equation and check your answer. $$ 1.1 z-2.5=0.3(z-2) $$

Find the slope-intercept form for the line satisfying the conditions. Parallel to the line \(y=-\frac{3}{4}(x-100)-99\) passing through \((1,3)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ -\frac{3}{4}<\frac{2-t}{5}<\frac{3}{4} $$

Exercises \(33-38:\) Write a formula for a linear function f whose graph satisfies the conditions. Slope 1.68 , passing through \((0,1.23)\)

Solve the absolute value equation. $$\left|\frac{3}{4} x-\frac{1}{4}\right|=\left|\frac{3}{4}-\frac{1}{4} x\right|$$

Solve the equation and check your answer. $$ 0.15 t+0.85(100-t)=0.45(100) $$

Find the slope-intercept form for the line satisfying the conditions. Perpendicular to the line \(y=-\frac{2}{3}(x-1980)+5\) passing through \((1980,10)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ \frac{1}{2} z+\frac{2}{3}(3-z)-\frac{5}{4} z \geq \frac{3}{4}(z-2)+z $$

Exercises \(33-38:\) Write a formula for a linear function f whose graph satisfies the conditions. Slope 0.5, passing through \((1,4.5)\)

Solve the absolute value equation. $$\left|\frac{1}{2} x+\frac{3}{2}\right|=\left|\frac{3}{2} x-\frac{7}{2}\right|$$

Solve the equation and check your answer. $$ 0.35 t+0.65(10-t)=0.55(10) $$

Find the slope-intercept form for the line satisfying the conditions. Perpendicular to \(y=6 x-10,\) passing through \((15,-7)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ \frac{2}{3}(1-2 z)-\frac{3}{2} z+\frac{5}{6} z \geq \frac{2 z-1}{3}+1 $$

Exercises \(33-38:\) Write a formula for a linear function f whose graph satisfies the conditions. Slope \(-2,\) passing through \((-1,5)\)

Solve the absolute value equation. $$|15 x-5|=|35-5 x|$$

Exercises \(39-48:\) Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 5 x-1=5 x+4 $$

Solve the inequality graphically. Use set-builder notation. $$ x+2 \geq 2 x $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=10 $$

Solve the absolute value equation. $$|20 x-40|=|80 x-20|$$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 7-9 z=2(3-4 z)-z $$

Find the slope-intercept form for the line satisfying the conditions. Parallel to \(y=-4 x-\frac{1}{4},\) passing through \((2,-5)\)

Solve the inequality graphically. Use set-builder notation. $$ 2 x-1 \leq x $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=-5 $$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 3(x-1)=5 $$

Find the slope-intercept form for the line satisfying the conditions. Perpendicular to \(y=-2 x,\) passing through \((-2,5)\)

Solve the inequality graphically. Use set-builder notation. $$ \frac{2}{3} x-2>-\frac{4}{3} x+4 $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=-\frac{1}{4} x $$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 22=-2(2 x+1.4) $$

Find the slope-intercept form for the line satisfying the conditions. Perpendicular to \(y=-\frac{6}{7} x+\frac{3}{7},\) passing through \((3,8)\)

Solve the inequality graphically. Use set-builder notation. $$ -2 x \geq-\frac{5}{3} x+1 $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=\frac{5}{3} x $$

Solve each equation or inequality. (a) \(|2 x-3|=1\) (b) \(|2 x-3|<1\) (c) \(|2 x-3|>1\)

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 0.5(x-2)+5=0.5 x+4 $$

Find the slope-intercept form for the line satisfying the conditions. Perpendicular to \(x+y=4,\) passing through \((15,-5)\)

Solve the inequality graphically. Use set-builder notation. $$ -1 \leq 2 x-1 \leq 3 $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=4-3 x $$

Solve each equation or inequality. (a) \(|5-x|=2\) (b) \(|5-x| \leq 2\) (c) \(|5-x| \geq 2\)

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ \frac{1}{2} x-2(x-1)=-\frac{3}{2} x+2 $$

Find the slope-intercept form for the line satisfying the conditions. Parallel to \(2 x-3 y=-6,\) passing through \((4,-9)\)

Solve the inequality graphically. Use set-builder notation. $$ -2<1-x<2 $$

Exercises \(39-44\) : Average Rate of Change Find the average rate of change of \(f\) from \(-2\) to \(2 .\) What is the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\), where \(x_{1} \neq x_{2} ?\) $$ f(x)=5 x+1 $$

Solve the equation (a) graphically, (b) numerically, and (c) symbolically. Then solve the nelated inequality. $$|2 x-5|=10, \quad|2 x-5|<10$$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ \frac{t+1}{2}=\frac{3 t-2}{6} $$

Find the slope-intercept form for the line satisfying the conditions. Parallel to \(2 x-3 y=-6,\) passing through \((4,-9)\)

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ \frac{2 x+1}{3}=\frac{2 x-1}{3} $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \((1990,4)\) and parallel to the line passing through \((1980,3)\) and \((2000,8)\)

Solve the inequality graphically. Use set-builder notation. $$ -1 \leq 1-2 x<5 $$

Solve the equation (a) graphically, (b) numerically, and (c) symbolically. Then solve the nelated inequality. $$|5-3 x|=2, \quad|5-3 x|>2$$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ \frac{1-2 x}{4}=\frac{3 x-1.5}{-6} $$