Chapter 1

Find the real solution(s) of the radical equation. Check your solutions. \(x+\sqrt{31-9 x}=5\)

Use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ 10.4 x^{2}+8.6 x+1.2=0 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ (x+5)^{2}=20 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ 0.60 x+0.40(100-x)=50 $$

Solve the inequality. Then graph the solution set on the real number line. \(-10 x<40\)

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

Use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ 7.06 x^{2}-4.85 x+0.50=0 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 12 x^{2}=300 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ x+8=2(x-2)-x $$

Solve the inequality. Then graph the solution set on the real number line. \(-6 x>15\)

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt{2 x+1}+x=7\)

Use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ 2 x^{2}-2.50 x-0.42=0 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 6 x^{2}=250 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ 3(x+3)=5(1-x)-1 $$

Solve the inequality. Then graph the solution set on the real number line. \(\frac{3}{5} x-7<8\)

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \((x-5)^{2 / 3}=16\)

Use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ -0.003 x^{2}+0.025 x-0.98=0 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 5 x^{2}=190 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{100-4 u}{3}=\frac{5 u+6}{4}+6 $$

Solve the inequality. Then graph the solution set on the real number line. \(\frac{5}{4} x+1 \leq 11\)

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \((x+3)^{4 / 3}=16\)

Use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ -0.005 x^{2}+0.101 x-0.193=0 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 15 x^{2}=620 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{17+y}{y}+\frac{32+y}{y}=100 $$

Find the domain of the expression. \(\sqrt{x^{2}-9}\)

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

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \((x+3)^{3 / 2}=8\)

In Exercises 37-46, solve the quadratic equation using any convenient method. $$ 2 x^{2}+7=2 x^{2}-x-4 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 3 x^{2}+2\left(x^{2}-4\right)=15 $$

Comparing Calories A lunch consisting of a Big Mac, large fries, and large soft drink at McDonald's contains 1440 calories. A lunch consisting of a small hamburger, small fries, and a small soft drink at McDonald's contains 660 calories. Find the percent change in calories from the larger to the smaller lunch. (Source: McDonald's Corporation)

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{5 x-4}{5 x+4}=\frac{2}{3} $$

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

Solve the inequality. Then graph the solution set on the real number line. \(6 x-4 \leq 2+8 x\)

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \(\left(x^{2}+2\right)^{2 / 3}=9\)

Solve the quadratic equation using any convenient method. $$ x^{2}-2 x+5=x^{2}-5 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ x^{2}+3\left(x^{2}-5\right)=10 $$

Comparing Calories One slice (or one-tenth) of a 14-inch Little Caesars pizza with bacon, pepperoni, Italian sausage, and extra cheese has 315 calories. The same slice without the extra toppings has 200 calories. Find the percent change in calories from a slice with the extra toppings to a slice without them. (Source: Little Caesars)

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{10 x+3}{5 x+6}=\frac{1}{2} $$

Find the domain of the expression. \(\sqrt[4]{6+x^{2}}\)

Solve the inequality. Then graph the solution set on the real number line. \(2 x-1 \geq 5 x\)

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \(\left(x^{2}-5\right)^{2 / 3}=16\)

Solve the quadratic equation using any convenient method. $$ 4 x^{2}-15=25 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 6 x^{2}-3\left(x^{2}+1\right)=23 $$

Salary You accept a new job with a starting salary of \(\$ 35,000\). You receive an \(8 \%\) raise at the start of your second year, a \(7.8 \%\) raise at the start of your third year, and a \(9.4 \%\) 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.) $$ 10-\frac{13}{x}=4+\frac{5}{x} $$

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

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

Find the real solution(s) of the equation involving rational exponents. Check your solutions. \(\left(x^{2}-x-22\right)^{4 / 3}=16\)

Solve the quadratic equation using any convenient method. $$ 3 x^{2}-16=38 $$

Solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ 2 x^{2}+5\left(x^{2}-2\right)=29 $$