Chapter 1

Solve equation by the square root property. $$ (5 x-1)^{2}=7 $$

An automobile repair shop charged a customer \(\$ 448,\) listing \(\$ 63\) for parts and the remainder for labor. If the cost of labor is \(\$ 35\) per hour, how many hours of labor did it take to repair the car?

Contain rational 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. $$\frac{4}{x}=\frac{5}{2 x}+3$$

Perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-16}+3 \sqrt{-81} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ -5 x \leq 30 $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$x^{\frac{3}{2}}=27$$

Solve equation by the square root property. $$ (8 x-3)^{2}=5 $$

A repair bill on a sailboat came to \(\$ 1603,\) including \(\$ 532\) for parts and the remainder for labor. If the cost of labor is \(\$ 63\) per hour, how many hours of labor did it take to repair the sailboat?

Contain rational 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. $$\frac{5}{x}=\frac{10}{3 x}+4$$

Perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-8}+3 \sqrt{-18} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 8 x-11 \leq 3 x-13 $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$(x-4)^{\frac{3}{2}}=27$$

Solve equation by the square root property. $$ (3 x-4)^{2}=8 $$

An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall." Using this description, what height corresponds to a recommended weight of 135 pounds?

Contain rational 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. $$ \frac{2}{x}+3=\frac{5}{2 x}+\frac{13}{4} $$

Perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-4})^{2} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 18 x+45 \leq 12 x-8 $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$(x+5)^{\frac{3}{2}}=8$$

Solve equation by the square root property. $$ (2 x+8)^{2}=27 $$

A job pays an annual salary of \(\$ 33,150,\) which includes a holiday bonus of \(\$ 750 .\) If paychecks are issued twice a month, what is the gross amount for each paycheck?

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

Perform the indicated operations and write the result in standard form. $$ (-5-\sqrt{-9})^{2} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 4(x+1)+2=3 x+6 $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$6 x^{\frac{5}{2}}-12=0$$

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

Perform the indicated operations and write the result in standard form. $$ (-3-\sqrt{-7})^{2} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 8 x+3>3(2 x+1)+x+5 $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$8 x^{\frac{5}{3}}-24=0$$

The rate for a particular international person-to-person telephone call is \(\$ 0.43\) for the first minute, \(\$ 0.32\) for each additional minute, and a \(\$ 2.10\) service charge. If the cost of a call is \(\$ 5.73,\) how long did the person talk?

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

Perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-11})^{2} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 2 x-11<-3(x+2) $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-10 x $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$(x-4)^{\frac{2}{3}}=16$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=l w\) for \(w\)

Perform the indicated operations and write the result in standard form. $$ \frac{-8+\sqrt{-32}}{24} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ -4(x+2)>3 x+20 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-14 x $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$(x+5)^{\frac{2}{3}}=4$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(D=R T\) for \(R\)

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

Perform the indicated operations and write the result in standard form. $$ \frac{-12+\sqrt{-28}}{32} $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 1-(x+3) \geq 4-2 x $$

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

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$\left(x^{2}-x-4\right)^{\frac{3}{4}}-2=6$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} b h\) for \(b\)

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

Perform the indicated operations and write the result in standard form. $$ \frac{-6-\sqrt{-12}}{48} $$

In all exercises, other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a mumber line. In Exercises \(27-50,\) solve each linear inequality. $$ 5(3-x) \leq 3 x-1 $$

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