Chapter 1

Solve each equation in Exercises \(15-26\) by the square root method. $$ (2 x+8)^{2}=27 $$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(-\infty, 3.5]$$

\- The International Panel on Climate Change is a U.N.sponsored body made up of more than 1500 leading experts from 60 nations. According to their recent findings, increased levels of atmospheric carbon dioxide are affecting our - climate. Global warming is under way and the effects could be catastrophic. The formula \(C=1.44 t+280\) models carbon dioxide concentration, \(C,\) in parts per million, \(t\) years after \(1939 .\) The preindustrial carbon dioxide concentration of 280 parts per million remained fairly constant until World War II, increasing after that due primarily to the burning of fossil fuels related to energy consumption. When will the concentration be double the preindustrial level? Round to the nearest year.

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x+1}{4}=\frac{1}{6}+\frac{2-x}{3} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{2+3 i}{2+i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \left|x^{2}+2 x-36\right|>12 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=x^{3}$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{3 \sqrt{x+1}}=\sqrt{3 x-5} $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+12 x $$

Two of the most expensive movies ever made were Titanic and Waterworld. The cost to make Titanic exceeded the cost to make Waterworld by \(\$ 40\) million. The combined cost to make the two movies was \(\$ 360\) million. Find the cost of making each of these movies.

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$5 x+11<26$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{4}=2+\frac{x-3}{3} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{3-4 i}{4+3 i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \left|x^{2}+6 x+1\right|>8 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=x^{3}-1$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{1+4 \sqrt{x}}=1+\sqrt{x} $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+16 x $$

In \(2001,\) the most populous countrics in the world were China and India. In that year, China's population exceeded India's by 260 million. Combined, the two countries had a population of 2310 million. Determine the 2001 population for China and India.

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$2 x+5<17$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ 5+\frac{x-2}{3}=\frac{x+3}{8} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\sqrt{-64}-\sqrt{-25}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x-4}{x+3}>0 $$

Solve and check each equation with rational exponents. $$ x^{3 / 2}=8 $$

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$3 x-7 \geq 13$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x+1}{3}=5-\frac{x+2}{7} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\sqrt{-81}-\sqrt{-144}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+5}{x-2}>0 $$

Solve and check each equation with rational exponents. $$ x^{3 / 2}=27 $$

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$8 x-2 \geq 14$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{3 x}{5}-\frac{x-3}{2}=\frac{x+2}{3} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-16}+3 \sqrt{-81}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+3}{x+4}<0 $$

Solve and check each equation with rational exponents. $$ (x-4)^{3 / 2}=27 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+3 x $$

A car rental agency charges \(\$ 200\) per week plus \(\$ 0.15\) per mile to rent a car. How many miles can you travel in one week for \(\$ 320 ?\)

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$-9 x \geq 36$$

Exercises \(31-50\) contain equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$ \frac{4}{x}=\frac{5}{2 x}+3 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-8}+3 \sqrt{-18}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+5}{x+2}<0 $$

Solve and check each equation with rational exponents. $$ (x+5)^{3 / 2}=8 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+5 x $$

A car rental agency charges \(\$ 180\) per week plus \(\$ 0.25\) per mile to rent a car. How many miles can you travel in one week for \(\$ 395 ?\)

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$-5 x \leq 30$$

Exercises \(31-50\) contain equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$ \frac{5}{x}=\frac{10}{3 x}+4 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-2+\sqrt{-4})^{2}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{-x+2}{x-4} \geq 0 $$

Solve and check each equation with rational exponents. $$ (x+5)^{3 / 2}=8 $$

According to the National Center for Health Statistics, in \(1990,28 \%\) of babies in the United States were born to parents who were not married. Throughout the 1990 s, this increased by approximately \(0.6 \%\) per year. Use this information to solve Exercises \(33-34\) If this trend continues, in which year will \(37 \%\) of babies be born out of wedlock?

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$8 x-11 \leq 3 x-13$$

Exercises \(31-50\) contain equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$ \frac{2}{x}+3=\frac{5}{2 x}+\frac{13}{4} $$