Chapter 1

Salary You accept a new job with a starting salary of \(\$ 48,000\). You receive a \(4 \%\) raise at the start of your second year, a \(5.5 \%\) raise at the start of your third year, and an \(11.4 \%\) raise at the start of your fourth year. (a) Find your salary for the second year. (b) Find your salary for the third year. (c) Find your salary for the fourth year.

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{15}{x}-4=\frac{6}{x}+3 $$

Find the domain of the expression. \(\sqrt{81-4 x^{2}}\)

Solve the inequality. Then graph the solution set on the real number line. \(3(x+2)+7<2 x-5\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{1}{x}-\frac{1}{x+1}=3\)

Solve the quadratic equation using any convenient method. $$ x^{2}+3 x+1=0 $$

In Exercises 41-62, solve the quadratic equation using any convenient method. \(x^{2}=64\)

World Internet Users The number of Internet users in the world reached 500 million in 2001 . By the end of 2003 , the number increased \(43.8 \%\). By the end of 2004 , the number increased \(13.6 \%\) from \(2003 .\) By the end of 2006 the number increased \(33.8 \%\) from 2004. (Source: Internet World Stats) (a) Find the number of users at the end of 2003 . (b) Find the number of users at the end of 2004 . (c) Find the number of users at the end of 2006 . (d) Find the percent increase in the number of users from 2001 to 2006 .

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{1}{x-3}+\frac{1}{x+3}=\frac{10}{x^{2}-9} $$

Find the domain of the expression. \(\sqrt{147-3 x^{2}}\)

Solve the inequality. Then graph the solution set on the real number line. \(2(x+7)-4 \geq 5(x-3)\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{x}{x^{2}-4}+\frac{1}{x+2}=3\)

Solve the quadratic equation using any convenient method. \(7 x^{2}=32\)

Sporting Goods Sales In 2002, the total sales of sporting goods in the United States was \(\$ 77,726,000,000\). In 2003 , the total sales increased \(2.6 \%\) from 2002 . In 2004 , the total sales increased \(6.1 \%\) from 2003 . In 2005, the total sales increased \(2.5 \%\) from 2004. (Source: National Sporting Goods Association) (a) Find the total sporting goods sales in 2003 . (b) Find the total sporting goods sales in 2004 . (c) Find the total sporting goods sales in 2005 . (d) Find the percent increase in total sales from 2002 to \(2005 .\)

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{1}{x-2}+\frac{3}{x+3}=\frac{4}{x^{2}+x-6} $$

Find the domain of the expression. \(\sqrt{x^{2}-7 x+10}\)

Solve the inequality. Then graph the solution set on the real number line. \(-3(x-1)+7<2 x+8\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{20-x}{x}=x\)

Solve the quadratic equation using any convenient method. \(x^{2}-2 x+1=0\)

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{6}{(x-3)(x-1)}=\frac{3}{x-3}+\frac{4}{x-1} $$

Find the domain of the expression. \(\sqrt{12-x-x^{2}}\)

Solve the inequality. Then graph the solution set on the real number line. \(5-3 x>-5(x+4)+6\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{4}{x}-\frac{5}{3}=\frac{x}{6}\)

Solve the quadratic equation using any convenient method. \(x^{2}-6 x+5=0\)

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{2}{(x-4)(x-2)}=\frac{1}{x-4}+\frac{2}{x-2} $$

Find the domain of the expression. \(\sqrt{x^{2}-3 x+3}\)

Solve the inequality. Then graph the solution set on the real number line. \(3 \leq 2 x-1<7\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{1}{x}=\frac{4}{x-1}+1\)

Solve the quadratic equation using any convenient method. \(16 x^{2}-9=0\)

Geometry A room is \(1.5\) times as long as it is wide, and its perimeter is 75 feet (see figure). Find the dimensions of the room.

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{7}{2 x+1}-\frac{8 x}{2 x-1}=-4 $$

Find the domain of the expression. \(\sqrt[4]{-x^{2}+2 x-2}\)

Solve the inequality. Then graph the solution set on the real number line. \(3>1-\frac{x}{2}>-3\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(x+\frac{9}{x+1}=5\)

Solve the quadratic equation using any convenient method. \(11 x^{2}+33 x=0\)

Geometry A picture frame has a total perimeter of 3 feet (see figure). The width of the frame is \(0.62\) times its length. Find the dimensions of the frame.

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{4}{u-1}+\frac{6}{3 u+1}=\frac{15}{3 u+1} $$

Consider the domains of the expressions \(\sqrt[3]{x^{2}-7 x+12}\) and \(\sqrt{x^{2}-7 x+12}\). Explain why the domain of \(\sqrt[3]{x^{2}-7 x+12}\) consists of all real numbers.

Solve the inequality. Then graph the solution set on the real number line. \(1<2 x+3<9\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{4}{x+1}-\frac{3}{x+2}=1\)

Writing Real-Life Problems In Exercises 47-50, solve the number problem and write a real-life problem that could be represented by this verbal model. For instance, an applied problem that could be represented by Exercise 47 is as follows. The sum of the length and width of a one-story house is 100 feet. The house has 2500 square feet of floor space. What are the length and width of the house? Find two numbers whose sum is 100 and whose product is 2500 .

Solve the quadratic equation using any convenient method. \(4 x^{2}-12 x+9=0\)

Simple Interest You invest \(\$ 2500\) at \(7 \%\) simple interest. How many years will it take for the investment to earn \(\$ 1000\) in interest?

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{3}{x(x-3)}+\frac{4}{x}=\frac{1}{x-3} $$

Consider the domains of the expressions \(\sqrt[3]{x^{2}-7 x+12}\) and \(\sqrt{x^{2}-7 x+12}\). Explain why the domain of \(\sqrt{x^{2}-7 x+12}\) is different from the domain of \(\sqrt[3]{x^{2}-7 x+12}\)

Solve the inequality. Then graph the solution set on the real number line. \(-8 \leq 1-3(x-2)<13\)

Find the real solution(s) of the equation involving fractions. Check your solutions. \(\frac{x+1}{3}-\frac{x+1}{x+2}=0\)

Writing Real-Life Problems In Exercises 47-50, solve the number problem and write a real-life problem that could be represented by this verbal model. For instance, an applied problem that could be represented by Exercise 47 is as follows. The sum of the length and width of a one-story house is 100 feet. The house has 2500 square feet of floor space. What are the length and width of the house? One number is 1 more than another number. The product of the two numbers is 72 . Find the numbers.

Solve the quadratic equation using any convenient method. \(x^{2}-14 x+49=0\)

Simple Interest An investment earns \(\$ 3200\) interest over a seven-year period. What is the rate of simple interest on a \(\$ 4800\) principal investment?