Chapter 1

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x-11 \leq 3 x-13$$

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

After a \(30 \%\) reduction, you purchase a dictionary for \(\$ 30.80\) What was the dictionary's price before the reduction?

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ (2 x+8)^{2}=27 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$18 x+45 \leq 12 x-8$$

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

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

Including \(8 \%\) sales tax, an inn charges \(\$ 162\) per night. Find the inn's nightly cost before the tax is added.

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+12 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$4(x+1)+2 \geq 3 x+6$$

Solve each equation with rational exponents. 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. \(\frac{2}{3 x}+\frac{1}{4}=\frac{11}{6 x}-\frac{1}{3}\)

Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+16 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x+3>3(2 x+1)+x+5$$

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

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

Involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item. The selling price of a refrigerator is \(\$ 584 .\) If the markup is \(25 \%\) of the dealer's cost, what is the dealer's cost of the refrigerator?

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-10 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$2 x-11<-3(x+2)$$

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

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. \(\frac{x-2}{2 x}+1=\frac{x+1}{x}\)

Involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item. The selling price of a scientific calculator is \(\$ 15 .\) If the markup is \(25 \%\) of the dealer's cost, what is the dealer's cost of the calculator?

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-14 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$-4(x+2)>3 x+20$$

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

You invested \(\$ 7000\) in two accounts paying \(6 \%\) and \(8 \%\) annual interest. If the total interest earned for the year was \(\$ 520,\) how much was invested at each rate?

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+3 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$1-(x+3) \geq 4-2 x$$

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

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

You invested \(\$ 11.000\) in two accounts paying \(5 \%\) and \(8 \%\) annual interest. If the total interest earned for the year was \(\$ 730,\) how much was invested at each rate?

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+5 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$5(3-x) \leq 3 x-1$$

Solve each equation with rational exponents. Check all proposed solutions. $$ \left(x^{2}-3 x+3\right)^{\frac{3}{2}}-1=0 $$

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

Things did not go quite as planned. You invested \(\$ 8000\), part of it in stock that paid \(12 \%\) annual interest. However, the rest of the money suffered a \(5 \%\) loss. If the total annual income from both investments was \(\$ 620,\) how much was invested at each rate?

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

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-7 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{x}{4}-\frac{3}{2} \leq \frac{x}{2}+1$$

By making an appropriate substitution. $$ x^{4}-5 x^{2}+4=0 $$

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. \(\frac{8 x}{x+1}=4-\frac{8}{x+1}\)

Things did not go quite as planned. You invested \(\$ 12,000\), part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?