Chapter 1

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ 2 x-6 \leq-18 \text { and } 2 x \geq-18 $$

Solve each problem. Randall wants to mix 50 lb of nuts worth \(\$ 2\) per \(\mathrm{lb}\) with some nuts worth \(\$ 6\) per \(\mathrm{lb}\) to make a mixture worth \(\$ 5\) per \(1 \mathrm{~b}\). How many pounds of \(\$ 6\) nuts must he use?

Solve each equation or inequality. Graph the solution set. $$ |-6 x-6| \leq 1 $$

Solve each equation, and check the solution. \(\frac{x-10}{5}+\frac{2}{5}=-\frac{x}{3}\)

Solve each inequality. Graph the solution set, and write it using interval notation. \(-4 \leq \frac{2-4 x}{3} \leq 0\)

Solve each equation, and check the solution. \(\frac{5-x}{6}+\frac{5}{6}=\frac{x}{54}\)

Give, in interval notation, the unknown numbers in each description. A number is between 0 and 1

Solve each equation, and check the solution. \(\frac{3 x-1}{4}+\frac{x+3}{6}=3\)

Give, in interval notation, the unknown numbers in each description. A number is between -3 and -2 .

Solve each equation or inequality. Graph the solution set. $$ |-4+x| \leq 9 $$

Solve each equation, and check the solution. \(\frac{3 x+2}{7}-\frac{x+4}{5}=2\)

Give, in interval notation, the unknown numbers in each description. Six times a number is between -12 and 12 .

Solve each equation or inequality. Graph the solution set. $$ |10-12 x| \geq 4 $$

Solve each equation, and check the solution. \(\frac{4 x+1}{3}=\frac{x+5}{6}+\frac{x-3}{6}\)

Solve each equation or inequality. Graph the solution set. $$ |8-10 x| \geq 2 $$

Solve each equation, and check the solution. \(\frac{2 x+5}{5}=\frac{3 x+1}{2}+\frac{-x+8}{16}\)

After 1 yr on the job, Grady got a raise from \(\$ 10.50\) per hour to \(\$ 11.76\) per hour. What was the percent increase in his hourly wage?

Give, in interval notation, the unknown numbers in each description. When 1 is added to twice a number, the result is greater than or equal to \(7 .\)

Solve each equation, and check the solution. \(0.04 x+0.06+0.03 x=0.03 x+1.46\)

Give, in interval notation, the unknown numbers in each description. If 8 is subtracted from a number, then the result is at least \(5 .\)

Solve each equation, and check the solution. \(0.05 x+0.08+0.06 x=0.07 x+0.68\)

Between 2000 and \(2016,\) the estimated population of metro New Orleans, Louisiana, declined from 1,337,726 to \(1,268,883 .\) What was the percent decrease to the nearest tenth?

Give, in interval notation, the unknown numbers in each description. One third of a number is added to 6 , giving a result of at least 3 .

Solve each equation, and check the solution. \(0.006 x-0.02 x+0.03=0.008 x+0.25\)

Between 2000 and \(2016,\) the estimated population of metro Chicago, Illinois, grew from 9,098,316 to \(9,512,999 .\) What was the percent increase to the nearest tenth?

Give, in interval notation, the unknown numbers in each description. Three times a number, minus \(5,\) is no more than 7 .

Solve each equation, and check the solution. \(0.05 x-0.1 x+0.6=0.04 x+2.22\)

The movie Transformers: The Last Knight in DVD was on sale for $16.17. The list price (full price) of this disc was 17.99.To the nearest tenth, what was the percent discount?

Bonnie earned scores of 90 and 82 on her first two tests in English literature. What score must she make on her third test to keep an average of 84 or greater?

Solve each equation, and check the solution. \(0.05 x+0.12(x+5000)=940\)

The Jurassic Park Collection in Blu-Ray was on sale for $29.96 . The list price (full price) of this three-disc set was 44.98. To the nearest tenth, what was the percent discount?

Scott scored 92 and 96 on his first two tests in "Methods in Teaching Mathematics." What score must he make on his third test to keep an average of 90 or greater?

Solve each equation, and check the solution. \(0.09 x+0.13(x+300)=61\)

To earn a \(\mathrm{B}\) in an algebra course requires an average of at least 80 on five tests. A student has scores of \(75,91,82,\) and \(74 .\) What possible scores on the fifth test would guarantee this student a \(\mathrm{B}\) in the class?

Solve each equation or inequality. Graph the solution set. $$ 3|x-6|=9 $$

Solve each equation, and check the solution. \(0.02(50)+0.08 x=0.04(50+x)\)

To pass Algebra II requires an average of at least 70 on four tests. A student has scores of \(80,62,\) and \(73 .\) What possible scores on the fourth test would guarantee this student a passing score in the class?

Solve each equation or inequality. Graph the solution set. $$ 5|x-4|=5 $$

Solve each equation, and check the solution. \(0.04(90)+0.12 x=0.06(460+x)\)

Latrice is signing up for cell phone service She must decide between Plan A, which costs \(\$ 54.99\) per month with a free phone included, and Plan B, which costs \(\$ 49.99\) per month, but would require her to buy a phone for \(\$ 129 .\) Under either plan, she does not expect to go over the included number of monthly minutes. After how many months would Plan \(B\) be a better deal?

Solve each equation or inequality. Graph the solution set. $$ |2-0.2 x|=2 $$

Solve each equation, and check the solution. \(0.05 x+0.10(200-x)=0.45 x\)

Newlyweds Bryce and Lauren need to move their belongings to their new apartment. They can rent a truck from U-Haul for \(\$ 29.95\) per day plus 28 cents per mile or from Budget Truck Rentals for \(\$ 34.95\) per day plus 25 cents per mile. After how many miles (to the nearest mile) would the Budget rental be a better deal than the U-Haul rental?

Solve each equation or inequality. Graph the solution set. $$ |5-0.5 x|=4 $$

Solve each equation, and check the solution. \(0.08 x+0.12(260-x)=0.48 x\)

The average monthly precipitation for Dallas, TX, for October, November, and December is 3.47 in. If 2.88 in. falls in October and 3.13 in. falls in November, how many inches must fall in December so that the average monthly precipitation for these months exceeds 3.47 in.?

Solve each equation or inequality. $$ |x|-1=4 $$

Solve each equation, and check the solution. \(0.006(x+2)=0.007 x+0.009\)

The average monthly precipitation for Honolulu, HI, for October, November, and December is 3.11 in. If 2.98 in. falls in October and 3.05 in. falls in November, how many inches must fall in December so that the average monthly precipitation for these months exceeds 3.11 in.?

Solve each equation or inequality. $$ |x|+3=10 $$