Chapter 1

Solve each problem involving consecutive integers. Find three consecutive odd integers such that the sum of the least integer and the greatest integer is 13 more than the middle integer.

Solve each investment problem. Mario earned \(\$ 12,000\) last year giving tennis lessons. He invested part of the money at \(3 \%\) simple interest and the rest at \(4 \% .\) In one year, he earned a total of \(\$ 440\) in interest. How much did he invest at each rate?

A jar of 20 coins contains 4 pennies. What percent of the coins are pennies?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |3-x| \leq 5 $$

To solve the following linear equation, we multiply each side by the least common denominator of all the fractions in the equation. What is this \(L C D ?\) $$ \frac{3}{4} x-\frac{1}{3} x=\frac{5}{6} x-5 $$

Solve each investment problem. Sheryl won \(\$ 60,000\) on a slot machine in Las Vegas. She invested part of the money at \(2 \%\) simple interest and the rest at \(3 \%\). In one year, she earned a total of \(\$ 1600\) in interest. How much was invested at each rate?

A closet containing 50 shoes has 12 that are black. What percent of the shoes are black?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |5-x| \leq 3 $$

Suppose that in solving the following equation, we multiply each side by \(12,\) rather than the least common denominator, \(6 .\) Would we obtain the correct solution? Explain. $$ \frac{1}{3} x+\frac{1}{2} x=\frac{1}{6} x $$

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ [-9,1] \cup(-\infty,-3) $$

Solve each investment problem. Michelle invested some money at \(4.5 \%\) simple interest and \(\$ 1000\) less than twice this amount at \(3 \%\). Her total annual income from the interest was \(\$ 1020\). How much was invested at each rate?

In a group of 12 children, 3 are girls. What percent are not girls?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |-5 x+3|<12 $$

To solve a linear equation with decimals, we usually begin by multiplying by a power of 10 so that all coefficients are integers. What is the least power of 10 that will accomplish this goal in each equation? (a) \(0.05 x+0.12(x+5000)=940\) (b) \(0.006(x+2)=0.007 x+0.009\)

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ [3,6] \cup(4,9) $$

Solve each investment problem. Plotr invested some money at \(3.5 \%\) simple interest, and \(\$ 5000\) more than three times this amount at \(4 \%\). He earned \(\$ 1440\) in annual interest. How much did he invest at each rate?

In a flock of 30 geese, 15 are male. What percent are not male?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |-2 x-4|<5 $$

The expression \(0.06(10-x)(100)\) is equivalent to which one of the following? A. \(0.06-0.06 x\) B. \(60-6 x\) C. \(6-6 x\) D. \(6-0.06 x\)

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ [-1,2] \cup(0,5) $$

A mixture of alcohol and water contains a total of 36 oz of liquid. There are 9 oz of pure alcohol in the mixture. What percent of the mixture is water? What percent is alcohol?

Solve each equation, and check the solution. \(-\frac{5}{9} x=2\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x<-1 \text { and } x>-5 $$

Solve each investment problem. Mona received a year-end bonus of \(\$ 17,000\) from her company and invested the money in an account paying \(6.5 \%\). How much additional money should she deposit in an account paying \(5 \%\) so that the return on the two investments will be \(6 \% ?\)

A mixture of acid and water is \(35 \%\) acid. If the mixture contains a total of \(40 \mathrm{~L},\) how many liters of pure acid are in the mixture? How many liters of pure water are in the mixture?

Solve each equation, and check the solution. \(\frac{3}{11} x=-5\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x>-1 \text { and } x<7 $$

Solve each problem. How many liters of a \(10 \%\) acid solution must be mixed with \(10 \mathrm{~L}\) of a \(4 \%\) solution to obtain a \(6 \%\) solution?

A real-estate agent earned \(\$ 6300\) commission on a property sale of \(\$ 210,000 .\) What is her rate of commission?

Solve each equation or inequality. Graph the solution set. $$ |3 x+2|<11 $$

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

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x<4 \text { or } x<-2 $$

Solve each problem. How many liters of a \(14 \%\) alcohol solution must be mixed with \(20 \mathrm{~L}\) of a \(50 \%\) solution to obtain a \(30 \%\) solution?

A certificate of deposit for 1 yr pays $25.50 simple interest on a principal of 3400. What is the interest rate being paid on this deposit?

Solve each equation, and check the solution. \(-\frac{7}{8} x=6\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x<5 \text { or } x<-3 $$

Solve each problem. In a chemistry class, 12 L of a \(12 \%\) alcohol solution must be mixed with a \(20 \%\) solution to obtain a \(14 \%\) solution. How many liters of the \(20 \%\) solution are needed?

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

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ -3 x \leq-6 \text { or }-3 x \geq 0 $$

Solve each problem. How many liters of a \(10 \%\) alcohol solution must be mixed with \(40 \mathrm{~L}\) of a \(50 \%\) solution to obtain a \(40 \%\) solution?

Solve each inequality. Graph the solution set, and write it using interval notation. \(-4<\frac{2}{3} x<12\)

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

Solve each problem. How much pure dye must be added to 4 gal of a \(25 \%\) dye solution to increase the solution to \(40 \% ?\) (Hint: Pure dye is \(100 \%\) dye.).

Solve each inequality. Graph the solution set, and write it using interval notation. \(-1 \leq \frac{2 x-5}{6} \leq 5\)

Solve each equation or inequality. Graph the solution set. $$ |3 x-1| \leq 11 $$

Solve each equation, and check the solution. \(\frac{3 x}{4}+\frac{5 x}{2}=13\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x+1 \geq 5 \text { and } x-2 \leq 10 $$

Solve each problem. How much water must be added to 6 gal of a \(4 \%\) insecticide solution to reduce the concentration to \(3 \% ?\) (Hint: Water is \(0 \%\) insecticide.)

Solve each equation or inequality. Graph the solution set. $$ |2 x-6| \leq 6 $$

Solve each equation, and check the solution. \(\frac{8 x}{3}-\frac{x}{2}=-13\)