Chapter 1

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{1}{x+3}+\frac{5}{x^{2}-9}=\frac{2}{x-3} $$

A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value. All real numbers \(x\) less than 3 units from 0

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}<4 $$

Sharing a Job Candy and Tim share a paper route. It takes Candy 70 min to deliver all the papers, and it takes Tim 80 min. How long does it take the two when they work together?

Evaluate the expression and write the result in the form \(a+b i .\) $$ \sqrt{-3} \sqrt{-12} $$

1–54 ? Find all real solutions of the equation. $$ \sqrt{5-x}+1=x-2 $$

Find all real solutions of the equation. \(10 y^{2}-16 y+5=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{3}{x+4}=\frac{1}{x}+\frac{6 x+12}{x^{2}+4 x} $$

A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value. All real numbers \(x\) more than 2 units from 0

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2} \geq 9 $$

Sharing a Job Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone?

Evaluate the expression and write the result in the form \(a+b i .\) $$ \sqrt{\frac{1}{3}} \sqrt{-27} $$

1–54 ? Find all real solutions of the equation. $$ 2 x+\sqrt{x+1}=8 $$

Find all real solutions of the equation. \(25 x^{2}+70 x+49=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{1}{x}-\frac{2}{2 x+1}=\frac{1}{2 x^{2}+x} $$

A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value. All real numbers \(x\) at least 5 units from 7

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ -2 x^{2} \leq 4 $$

Sharing a Job \(\quad\) Betty and Karen have been hired to paint the houses in a new development. Working together the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 6 \(\mathrm{h}\) to paint a house alone. How long does it take Karen to paint a house working alone?

Evaluate the expression and write the result in the form \(a+b i .\) $$ (3-\sqrt{-5})(1+\sqrt{-1}) $$

1–54 ? Find all real solutions of the equation. $$ x-\sqrt{x+3}=\frac{x}{2} $$

Find all real solutions of the equation. \(3 x^{2}+2 x+2=0\)

\(47-70\) The given equation involves a power of the variable. Find all real solutions of the equation. $$ x^{2}=49 $$

A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value. All real numbers \(x\) at most 4 units from 2

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ (x+2)(x-1)(x-3) \leq 0 $$

Sharing a Job Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 20\(\%\) less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?

Evaluate the expression and write the result in the form \(a+b i .\) $$ \frac{1-\sqrt{-1}}{1+\sqrt{-1}} $$

1–54 ? Find all real solutions of the equation. $$ x+2 \sqrt{x-7}=10 $$

Find all real solutions of the equation. \(5 x^{2}-7 x+5=0\)

\(47-70\) The given equation involves a power of the variable. Find all real solutions of the equation. $$ x^{2}=18 $$

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{3}-4 x>0 $$

Distance, Speed, and Time Wendy took a trip from Davenport to Omaha, a distance of 300 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 40 \(\mathrm{mi} / \mathrm{h}\) and the train 60 \(\mathrm{mi} / \mathrm{h}\) . The entire trip took 5\(\frac{1}{2} \mathrm{h} .\) How long did Wendy spend on the train?

Evaluate the expression and write the result in the form \(a+b i .\) $$ \frac{2+\sqrt{-8}}{1+\sqrt{-2}} $$

1–54 ? Find all real solutions of the equation. $$ \sqrt{\sqrt{x+5}+x}=5 $$

Use the quadratic formula and a calculator to find all real solutions, correct to three decimals. \(x^{2}-0.011 x-0.064=0\)

\(47-70\) The given equation involves a power of the variable. Find all real solutions of the equation. $$ x^{2}-24=0 $$

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ 16 x \leq x^{3} $$

Distance, Speed, and Time Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 2 h later, at what average speed is each cyclist traveling?

Evaluate the expression and write the result in the form \(a+b i .\) $$ (\sqrt{3}-\sqrt{-4})(\sqrt{6}-\sqrt{-8}) $$

1–54 ? Find all real solutions of the equation. $$ \sqrt[3]{4 x^{2}-4 x}=x $$

Use the quadratic formula and a calculator to find all real solutions, correct to three decimals. \(x^{2}-2.450 x+1.500=0\)

\(47-70\) The given equation involves a power of the variable. Find all real solutions of the equation. $$ x^{2}-7=0 $$

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{x-3}{x+1} \geq 0 $$

Distance, Speed, and Time A pilot flew a jet from Montreal to Los Angeles, a distance of 2500 \(\mathrm{mi}\) . On the return trip the average speed was 20\(\%\) faster than the out- bound speed. The round-trip took 9 h 10 min. What was the speed from Montreal to Los Angeles?

Evaluate the expression and write the result in the form \(a+b i .\) $$ \frac{\sqrt{-36}}{\sqrt{-2} \sqrt{-9}} $$

1–54 ? Find all real solutions of the equation. $$ x^{2} \sqrt{x+3}=(x+3)^{3 / 2} $$

Use the quadratic formula and a calculator to find all real solutions, correct to three decimals. \(x^{2}-2.450 x+1.501=0\)

\(47-70\) The given equation involves a power of the variable. Find all real solutions of the equation. $$ 8 x^{2}-64=0 $$

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{2 x+6}{x-2}<0 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ \frac{\sqrt{-7} \sqrt{-49}}{\sqrt{28}} $$

1–54 ? Find all real solutions of the equation. $$ \sqrt{11-x^{2}}-\frac{2}{\sqrt{11-x^{2}}}=1 $$