Chapter 1

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

Exercises \(37-38\) involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item. 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?

Perform the indicated operations and write the result in standard form. $$ \frac{-15-\sqrt{-18}}{33} $$

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

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

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 \(\$ 8000,\) 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?

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

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

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}\)

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?

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

Perform the indicated operations and write the result in standard form. $$ \sqrt{-12}(\sqrt{-4}-\sqrt{2}) $$

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

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

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer ficld is 300 yards, what are its dimensions?

Perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-5})(-4 \sqrt{-12}) $$

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

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(7-\frac{4}{5} x<\frac{3}{5}\)

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-7})(2 \sqrt{-8}) $$

Solve each equation by making an appropriate substitution. $$4 x^{4}-13 x^{2}-9$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{x-4}{6} \geq \frac{x-2}{9}+\frac{5}{18}\)

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. $$ \frac{3}{x+2}+\frac{2}{x-2}-\frac{8}{(x+2)(x-2)} $$

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Perform the indicated operation(s) and write the result in standard form. $$ (2-3 i)(1-i)-(3-i)(3+i) $$

Solve each equation by making an appropriate substitution. $$x-13 \sqrt{x}+40-0$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{4 x-3}{6}+2 \geq \frac{2 x-1}{12}\)

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. $$ \frac{5}{x+2}+\frac{3}{x-2}-\frac{12}{(x+2)(x-2)} $$

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions? (IMAGE CANT COPY)

Perform the indicated operation(s) and write the result in standard form. $$ (8+9 i)(2-i)-(1-i)(1+i) $$

Solve each equation by making an appropriate substitution. $$2 x-7 \sqrt{x}-30-0$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(4(3 x-2)-3 x<3(1+3 x)-7\)

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

The rectangular painting in the figure shown measures 12 inches by 16 inches and is surrounded by a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 72 inches. Determine the width of the frame. (IMAGE CANT COPY)

Solve each equation in Exercises \(47-64\) by completing the square. $$x^{2}+6 x=7$$

Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is four more than twice the \(x\) -value.

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(3(x-8)-2(10-x)>5(x-1)\)

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. $$ \frac{4}{x+5}+\frac{2}{x-5}-\frac{32}{x^{2}-25} $$

The rectangular swimming pool in the figure shown measures 40 feet by 60 feet and is surrounded by a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 248 feet. Determine the width of the path. (IMAGE CANT COPY)

Solve each equation in Exercises \(47-64\) by completing the square. $$x^{2}+6 x=-8$$

Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is the difference between four and twice the \(x\) -value.

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(5(x-2)-3(x+4) \geq 2 x-20\)

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. $$ \frac{1}{x-4}-\frac{5}{x+2}-\frac{6}{x^{2}-2 x-8} $$

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?

Solve each equation in Exercises \(47-64\) by completing the square. $$x^{2}-2 x=2$$

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

Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is three decreased by the square of the \(x\) -value.

Solve each equation by making an appropriate substitution. $$x^{\frac{2}{3}}-x^{\frac{1}{3}}-6-0$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(6(x-1)-(4-x) \geq 7 x-8\)