Chapter 1

Solve each inequality. Graph the solution set on a number line. $$ |b-4| > 6 $$

Solve each inequality. Then graph the solution set on a number line. \(6 b+11 \geq 15\)

Name the sets of numbers to which each number belongs. $$ \frac{12}{2} $$

Write an algebraic expression to represent each verbal expression. four less than the square of a number 10

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(|2 b-15|\)

Evaluate each expression if \(a=3, b=0.3, c=\frac{1}{3},\) and \(d=-1\). \(\frac{d+4}{a^{2}+3}\)

Solve each inequality. Graph the solution set on a number line. $$ |3 w+2| \leq 5 $$

Solve each inequality. Then graph the solution set on a number line. \(2(4 t+9) \leq 18\)

Name the sets of numbers to which each number belongs. $$ \sqrt{121} $$

Write an algebraic expression to represent each verbal expression. the product of the cube of a number and \(-6\)

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(|4 a+7|\)

Evaluate each expression if \(a=3, b=0.3, c=\frac{1}{3},\) and \(d=-1\). \(\frac{1-b}{3 c-3 b}\)

Solve each inequality. Graph the solution set on a number line. $$ |6 r-3| < 21 $$

Solve each inequality. Then graph the solution set on a number line. \(90 \geq 5(2 r+6)\)

Name the sets of numbers to which each number belongs. $$ -\sqrt{36} $$

Write an algebraic expression to represent each verbal expression. five times the sum of 9 and a number

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(-|18-5 c|\)

SPED LIMITS For Exercises 22 and 23 , use the following information. On some interstate highways, the maximum speed a car may drive is 65 miles per hour. A tractor may not drive more than 55 miles per hour. The minimum speed for all vehicles is 45 miles per hour. Write an inequality to represent the allowable speed for a car on an interstate highway.

Solve each inequality. Then graph the solution set on a number line. \(\frac{3 t+6}{2}<3 t+6\)

Name the property illustrated by each equation. $$ 5 a+(-5 a)=0 $$

Write an algebraic expression to represent each verbal expression. twice the sum of a number and 8

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(-|2 c-a|\)

Air pollution can be reduced by riding a bicycle rather than driving a car. To find the number of pounds of pollutants created by starting a typical car 10 times and driving it for 50 miles, find the value of the expression \(\frac{(52.84 \times 10)+(5.955 \times 50)}{454}\).

SPED LIMITS For Exercises 22 and 23 , use the following information. On some interstate highways, the maximum speed a car may drive is 65 miles per hour. A tractor may not drive more than 55 miles per hour. The minimum speed for all vehicles is 45 miles per hour. Write an inequality to represent the speed at which a tractor-trailer may travel on an interstate highway.

Solve each inequality. Then graph the solution set on a number line. \(\frac{k+7}{3}-1<0\)

Name the property illustrated by each equation. $$ -6 x y+0=-6 x y $$

Solve each equation. Check your solutions. \(|x-25|=17\)

The formula for the area \(A\) of a circle with diameter \(d\) is \(A=\pi\left(\frac{d}{2}\right)^{2} .\) Write an expression to represent the area of the circle.

Solve each inequality. Graph the solution set on a number line. $$ -4 < 4 f+24 < 4 $$

Solve each inequality. Then graph the solution set on a number line. \(\frac{2 n-6}{5}+1>0\)

Name the property illustrated by each equation. $$ [5+(-2)]+(-4)=5+[-2+(-4)] $$

Write a verbal expression to represent each equation. \(2 n+3=-1\)

Solve each equation. Check your solutions. \(|y+9|=21\)

The formula for the volume \(V\) of a right circular cone with radius \(r\) and height \(h\) is \(V=\frac{1}{3} \pi r^{2} h .\) Write an expression for the volume of a cone with \(r=3 x\) and \(h=2 x\).

Solve each inequality. Graph the solution set on a number line. $$ a+2 > -2 \text { or } a-8 < 1 $$

David earns \(\$ 6.40\) an hour working at Box Office Videos. Each week 25\(\%\) of his total pay is deducted for taxes. If David wants his take-home pay to be at least \(\$ 120\) a week, solve \(6.4 x-0.25(6.4 x) \geq 120\) to determine how many hours he must work.

Name the property illustrated by each equation. $$ (2+14)+3=3+(2+14) $$

Write a verbal expression to represent each equation. \(y^{2}=4 y\)

Solve each equation. Check your solutions. \(33=|a+12|\)

Evaluate each expression if \(a=\frac{2}{5}, b=-3, c=0.5,\) and \(d=6\). \(b^{4}-d\)

Solve each inequality. Graph the solution set on a number line. $$ |-5 y| < 35 $$

Admission to a state fair is \(\$ 12\) per person. Bus parking costs \(\$ 20 .\) Solve \(12 n+20 \leq 600\) to determine how many people can go to the fair if a group has \(\$ 600\) and uses only one bus.

Name the property illustrated by each equation. $$ \left(1 \frac{2}{7}\right)\left(\frac{7}{9}\right)=1 $$

Write a verbal expression to represent each equation. \(3 a^{3}=a+4\)

Solve each equation. Check your solutions. \(11=|3 x+5|\)

Evaluate each expression if \(a=\frac{2}{5}, b=-3, c=0.5,\) and \(d=6\). \((5-d)^{2}+a\)

Define a variable and write an inequality for each problem. Then solve. The product of 12 and a number is greater than 36

Name the property illustrated by each equation. $$ 2 \sqrt{3}+5 \sqrt{3}=(2+5) \sqrt{3} $$

Name the property illustrated by each statement. If \([3(-2)] z=24,\) then \(-6 z=24\)

Solve each equation. Check your solutions. \(8|w-7|=72\)