Chapter 1

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

Solve each inequality. Graph the solution set on a number line. $$ |n| \geq n $$

Define a variable and write an inequality for each problem. Then solve. Three less than twice a number is at most 5 .

Identify the additive inverse and multiplicative inverse for each number. $$ -10 $$

Name the property illustrated by each statement. If \(5+b=13,\) then \(b=8\)

Solve each equation. Check your solutions. \(2|b+4|=48\)

Evaluate each expression if \(a=\frac{2}{5}, b=-3, c=0.5,\) and \(d=6\). \(\frac{2 b-15 a}{3 c}\)

Solve each inequality. Graph the solution set on a number line. $$ |n| \leq n $$

Define a variable and write an inequality for each problem. Then solve. The sum of a number and 8 is more than 2 .

Identify the additive inverse and multiplicative inverse for each number. $$ 2.5 $$

Name the property illustrated by each statement. If \(2 x=3 d\) and \(3 d=-4,\) then \(2 x=-4\)

Solve each equation. Check your solutions. \(0=|2 z-3|\)

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

Solve each inequality. Graph the solution set on a number line. $$ \frac{|2 n-7|}{3} \leq 0 $$

Define a variable and write an inequality for each problem. Then solve. The product of \(-4\) and a number is at least \(35 .\)

Identify the additive inverse and multiplicative inverse for each number. $$ -0.125 $$

Name the property illustrated by each statement. If \(y-2=-8,\) then \(3(y-2)=3(8)\)

Solve each equation. Check your solutions. \(|6 c-1|=0\)

Evaluate each expression if \(a=\frac{2}{5}, b=-3, c=0.5,\) and \(d=6\). \(\frac{1}{c}+\frac{1}{d}\)

Solve each inequality. Graph the solution set on a number line. $$ \frac{|n-3|}{2} < n $$

Define a variable and write an inequality for each problem. Then solve. The difference of one half of a number and 7 is greater than or equal to 5

Identify the additive inverse and multiplicative inverse for each number. $$ -\frac{5}{8} $$

Solve each equation. Check your solution. \(2 p=14\)

Solve each equation. Check your solutions. \(-12|9 x+1|=144\)

Find the value of \(a b^{n}\) if \(n=3, a=2000,\) and \(b=-\frac{1}{5}\)

Define a variable and write an inequality for each problem. Then solve. One more than the product of \(-3\) and a number is less than 16

Identify the additive inverse and multiplicative inverse for each number. $$ \frac{4}{3} $$

Solve each equation. Check your solution. \(-14+n=-6\)

Solve each equation. Check your solutions. \(1=|5 x+9|+6\)

Suppose you are about a mile from a fireworks display. You count 5 seconds between seeing the light and hearing the sound of the fireworks display. You estimate the viewing angle is about \(4^{\circ} .\) Using the information at the left, estimate the width of the firework display.

Solve each inequality. Then graph the solution set on a number line. \(14-8 n \leq 0\)

Identify the additive inverse and multiplicative inverse for each number. $$ -4 \frac{3}{5} $$

Solve each equation. Check your solution. \(7 a-3 a+2 a-a=16\)

Some say that to brew an excellent cup of coffee, you must have a brewing temperature of \(200^{\circ} \mathrm{F}\) , plus or minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

Solve each inequality. Then graph the solution set on a number line. \(-4(5 w-8)<33\)

Solve each equation. Check your solution. \(x+9 x-6 x+4 x=20\)

Before an election, a company conducts a telephone survey of likely voters. Based on their survey data, the polling company states that an amendment to the state constitution is supported by 59% of the state’s residents and that 41% of the state’s residents do not approve of the amendment. According to the company, the results of their survey have a margin of error of 3%. Write and solve an equation describing the maximum and minimum percent of the state’s residents that support the amendment.

A patient must take blood pressure medication that is dispensed in 125-milligram tablets. The dosage is 15 milligrams per kilogram of body weight and is given every 8 hours. If the patient weighs 25 kilograms, how many tablets would be needed for a 30-day supply? Use the formula \(n=[15 b \div(125 \times 8)] \times 24 d,\) where \(n\) is the number of tablets, \(d\) is the number of days the supply should last, and \(b\) is body weight in kilograms.

Solve each inequality. Then graph the solution set on a number line. \(0.02 x+5.58<0\)

BAKING Mitena is making two types of cookies. The first recipe calls for 2\(\frac{1}{4}\) cups of flour, and the second calls for 1\(\frac{1}{8}\) cups of flour. If she wants to make 3 batches of the first recipe and 2 batches of the second recipe, how many cups of flour will she need? Use the properties of real numbers to show how Mitena could compute this amount mentally. Justify each step.

Solve each equation. Check your solution. $$ 27=-9(y+5)+6(y+8) $$

Solve each equation. Check your solutions. \(35=7|4 x-13|\)

The formula for quarterback efficiency rating in the National Football League is \(\left(\frac{\frac{C}{A}-0.3}{0.2}+\frac{\frac{Y}{A}-3}{4}+\frac{\frac{T}{A}}{0.05}+\frac{0.095-\frac{I}{A}}{0.04}\right) \times \frac{100}{6},\) where \(C\) is the number of passes completed, A is the number of passes attempted, Y is passing yardage, T is the number of touchdown passes, and I is the number of interceptions. In 2005, Ben Roethlisberger of the Pittsburgh Steelers completed 168 of the 268 passes he attempted for 2385 yards. He threw 17 touchdowns and 9 interceptions. Find his efficiency rating for 2005.

Solve each inequality. Then graph the solution set on a number line. \(1.5-0.25 c<6\)

Simplify each expression. $$ 7 a+3 b-4 a-5 b $$

Solve each equation. Check your solution. $$ -7(p+7)+3(p-4)=-17 $$

Solve each equation. Check your solutions. \(-9=-3|2 n+5|\)

Write an algebraic expression in which subtraction is performed before division, and the symbols ( ), [ ], or { } are not used.

Solve each inequality. Then graph the solution set on a number line. \(6 d+3 \geq 5 d-2\)

Simplify each expression. $$ 3 x+5 y+7 x-3 y $$