Chapter 1

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-5-\sqrt{-9})^{2}$$

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. $$ \frac{-x-3}{x+2} \leq 0 $$

Solve and check each equation with rational exponents. $$ 8 x^{5 / 3}-24=0 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-9 x $$

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 \(40 \%\) 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. $$18 x+45 \leq 12 x-8$$

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. $$ \frac{7}{2 x}-\frac{5}{3 x}=\frac{22}{3} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-3-\sqrt{-7})^{2}$$

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. $$ \frac{4-2 x}{3 x+4} \leq 0 $$

Solve and check each equation with rational exponents. $$ (x-4)^{2 / 3}=16 $$

The bus fare in a city is \(\$ 1.25 .\) People who use the bus have the option of purchasing a monthly coupon book for \(\$ 21.00 .\) With the coupon book, the fare is reduced to \(\$ 0.50\) a. Let \(x\) represent the number of times in a month the bus is used. Write algebraic expressions for the total monthly costs of using the bus \(x\) times both with and without the coupon book. b. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$4(x+1)+2 \geq 3 x+6$$

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. $$ \frac{2}{3 x}+\frac{1}{4}=\frac{11}{6 x}-\frac{1}{3} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-2+\sqrt{-11})^{2}$$

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. $$ \frac{3 x+5}{6-2 x} \geq 0 $$

Solve and check each equation with rational exponents. $$ (x+5)^{2 / 3}=4 $$

A coupon book for a bridge costs \(\$ 21\) per month. The toll for the bridge is normally \(\$ 2.50,\) but it is reduced to \(\$ 1\) for people who have purchased the coupon book. a. Let \(x\) represent the number of times in a month the bridge is used. Write algebraic expressions for the total monthly costs of using the bridge \(x\) times both with and without the coupon book. b. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$8 x+3>3(2 x+1)+x+5$$

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. $$ \frac{5}{2 x}-\frac{8}{9}=\frac{1}{18}-\frac{1}{3 x} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-8+\sqrt{-32}}{24}$$

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. $$ \frac{x}{x-3}>0 $$

Solve and check each equation with rational exponents. $$ \left(x^{2}-x-4\right)^{3 / 4}-2=6 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{1}{3} x $$

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of \(\$ 100\) and you pay \(80 \%\) of the manufacturer's recommended list price. Plan B offers an annual membership fee of \(\$ 40\) and you pay \(90 \%\) of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$2 x-11<-3(x+2)$$

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. $$ \frac{x-2}{2 x}+1=\frac{x+1}{x} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-12+\sqrt{-28}}{32}$$

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. $$ \frac{x+4}{x}>0 $$

Solve and check each equation with rational exponents. $$ \left(x^{2}-3 x+3\right)^{3 / 2}-1=0 $$

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of \(\$ 300\) and you pay \(70 \%\) of the manufacturer's recommended list price. Plan B offers an annual membership fee of \(\$ 40\) and you pay \(90 \%\) of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$-4(x+2)>3 x+20$$

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. $$ \frac{4}{x}=\frac{9}{5}-\frac{7 x-4}{5 x} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-6-\sqrt{-12}}{48}$$

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. $$ \frac{x+1}{x+3}<2 $$

Solve each equation in by making an appropriate substitution. $$ x^{4}-5 x^{2}+4=0 $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}+6 x=7 $$

Your grandmother needs your help. She has \(\$ 50,000\) to invest. Part of this money is to be invested in noninsured bonds paying \(15 \%\) annual interest. The rest of this money is to be invested in a government-insured certificate of deposit paying \(7 \%\) annual interest. She told you that she requires \(\$ 6000\) per year in extra income from both of these investments. How much money should be placed in each investment?

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$1-(x+3) \geq 4-2 x$$

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. $$ \frac{1}{x-1}+5=\frac{11}{x-1} $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-15-\sqrt{-18}}{33}$$

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. $$ \frac{x}{x-1}>2 $$

Solve each equation in by making an appropriate substitution. $$ x^{4}-13 x^{2}+36=0 $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}+6 x=-8 $$

You inherit \(\$ 18,750\) with the stipulation that for the first year the money must be placed in two investments paying \(10 \%\) and \(12 \%\) annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $\$ 2117 ?

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$5(3-x) \leq 3 x-1$$

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. $$ \frac{3}{x+4}-7=\frac{-4}{x+4} $$

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

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. $$ \frac{x+4}{2 x-1} \leq 3 $$

Solve each equation in by making an appropriate substitution. $$ 9 x^{4}=25 x^{2}-16 $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}-2 x=2 $$