Chapter 2

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ -2(x-10)+1>0 $$

Exercises 11 and 12: Write a symbolic representation (formula) for a function \(f\) that computes the following. (a) The number of pounds in \(x\) ounces (b) The number of dimes in \(x\) dollars (c) The monthly electric bill in dollars if \(x\) kilowattbours are used at 6 cents per kilowatt-hour and there is a fee of \(\$ 6.50\) (d) The cost of skiing \(x\) times with a \(\$ 500\) season pass

Graph by hand. (a) Find the \(x\) -intercept. (b) Determine where the graph is increasing and where it is decreasing. $$ y=\left|\frac{1}{2} x+1\right| $$

Determine whether the equation is linear or nonlinear by trying to write it in the form ax \(+b=0\) $$ 2(x-3)=4-5 x $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ 3(x+5) \leq 0 $$

Exercises 11 and 12: Write a symbolic representation (formula) for a function \(f\) that computes the following. (a) The distance traveled by a car moving at 50 miles per hour for \(x\) hours (b) The total number of hours in day \(x\) (c) The distance in miles between a runner and home after \(x\) hours if the runner starts 1 mile from home and jogs away from home at 6 miles per hour (d) A car's speed in feet per second after \(x\) seconds if its tires are 2 feet in diameter and rotating 14 times per second

(Refer to Example \(1 .\) ) Do the following. (a) Graph \(y=f(x)\) (b) Use the graph of \(y=f(x)\) to sketch a graph of the equation \(y=|f(x)|\) (c) Determine the \(x\) -intercept for the \(\operatorname{graph}\) of the equation \(y=|f(x)|\) $$ y=2 x $$

Exercises \(13-38:\) Solve the equation and check your answer. $$ 2 x-8=0 $$

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

Solve the equation and check your answer. $$ 4 x-8=0 $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ \frac{2-t}{6}<0 $$

Solve the equation and check your answer. $$ -5 x+3=23 $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ 4 x-1<\frac{3-x}{-3} $$

Solve the equation and check your answer. $$ -9 x-3=24 $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ \frac{x+5}{-10}>2 x+3 $$

Solve the equation and check your answer. $$ 4(z-8)=z $$

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

Solve the equation and check your answer. $$ -3(2 z-1)=2 z $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ -\frac{1}{4}(2 z-6)+z \geq 5 $$

Solve the absolute value equation. $$ |-2 x|=4 $$

Solve the equation and check your answer. $$ -5(3-4 t)=65 $$

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ \frac{1-x}{4}<\frac{2 x-2}{3} $$

Match the equation to its graph \((a-f)\) shown in the next column. A.(GRAPH CANNOT COPY) B.(GRAPH CANNOT COPY) C.(GRAPH CANNOT COPY) D.(GRAPH CANNOT COPY) E.(GRAPH CANNOT COPY) F.(GRAPH CANNOT COPY) $$ \mathbf{x}=\mathbf{k}, \mathbf{k}>\mathbf{0} $$

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ f(x)=3 x+2 $$

Solve the equation and check your answer. $$ 6(5-3 t)=66 $$

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

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ f(x)=-\frac{3}{2} x $$

Solve the absolute value equation. $$|5 x-7|=2$$

Solve the equation and check your answer. $$ k+8=5 k-4 $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \((-1,-4)\) and \((1,2)\)

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

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ f(x)=\frac{1}{2} x-2 $$

Solve the absolute value equation. $$|-3 x-2|=5$$

Solve the equation and check your answer. $$ 2 k-3=k+3 $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \((-1,6)\) and \((2,-3)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ 5-(2-3 x) \leq-5 x $$

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ f(x)=3-x $$

Solve the absolute value equation. $$|3-4 x|=5$$

Solve the equation and check your answer. $$ 2(1-3 x)+1=3 x $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \((4,5)\) and \((1,-3)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ 5<4 t-1 \leq 11 $$

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ g(x)=-2 $$

Solve the absolute value equation. $$|2-3 x|=1$$

Solve the equation and check your answer. $$ 5(x-2)=-2(1-x) $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \((8,-2)\) and \((-2,3)\)

Solve the inequality symbolically. Express the solution set in set-builder or interval notation. $$ -1 \leq 2 t \leq 4 $$

Exercises \(19-32:\) Graph the linear function by hand. Identify the slope and y-intercept. $$ g(x)=20-10 x $$

Solve the absolute value equation. $$|-6 x-2|=0$$

Solve the equation and check your answer. $$ -5(3-2 x)-(1-x)=4(x-3) $$

Find the slope-intercept form for the line satisfying the conditions. y-intercept \(5,\) slope \(-7.8\)