Chapter 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?

Contain linear equations with constants in denominators. Solve each equation. $$\frac{3 x}{5}-x=\frac{x}{10}-\frac{5}{2}$$

Divide and express the result in standard form. $$ \frac{2 i}{1+i} $$

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

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{x+5}-\sqrt{x-3}=2$$

Solve equation by the square root property. $$ 3(x+4)^{2}=21 $$

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?

Contain linear equations with constants in denominators. Solve each equation. $$2 x-\frac{2 x}{7}=\frac{x}{2}+\frac{17}{2}$$

Divide and express the result in standard form. $$ \frac{5 i}{2-i} $$

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

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{x-5}-\sqrt{x-8}=3$$

Solve equation by the square root property. $$ (x+3)^{2}=-16 $$

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

Contain linear equations with constants in denominators. Solve each equation. $$\frac{x+3}{6}=\frac{3}{8}+\frac{x-5}{4}$$

Divide and express the result in standard form. $$ \frac{8 i}{4-3 i} $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1,0\) \(1,2,\) and 3. $$ y=9-x^{2} $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{2 x-3}-\sqrt{x-2}=1$$

Solve equation by the square root property. $$ (x-1)^{2}=-9 $$

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?

Contain linear equations with constants in denominators. Solve each equation. $$\frac{x+1}{4}=\frac{1}{6}+\frac{2-x}{3}$$

Divide and express the result in standard form. $$ \frac{-6 i}{3+2 i} $$

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

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. $$ 5 x+11<26 $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{2 x+3}+\sqrt{x-2}=2$$

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

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?

Contain linear equations with constants in denominators. Solve each equation. $$\frac{x}{4}=2+\frac{x-3}{3}$$

Divide and express the result in standard form. $$ \frac{2+3 i}{2+i} $$

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

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. $$ 2 x+5<17 $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{x+2}+\sqrt{3 x+7}=1$$

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

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?

Contain linear equations with constants in denominators. Solve each equation. $$5+\frac{x-2}{3}=\frac{x+3}{8}$$

Divide and express the result in standard form. $$ \frac{3-4 i}{4+3 i} $$

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

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. $$ 3 x-7 \geq 13 $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $\sqrt{3 \sqrt{x+1}}=\sqrt{3 x-5}$$

Solve equation by the square root property. $$ (3 x+2)^{2}=9 $$

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.

Contain linear equations with constants in denominators. Solve each equation. $$\frac{x+1}{3}=5-\frac{x+2}{7}$$

Perform the indicated operations and write the result in standard form. $$ \sqrt{-64}-\sqrt{-25} $$

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. $$ 8 x-2 \geq 14 $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{1+4 \sqrt{x}}=1+\sqrt{x}$$

Solve equation by the square root property. $$ (4 x-1)^{2}=16 $$

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.

Contain linear equations with constants in denominators. Solve each equation. $$\frac{3 x}{5}-\frac{x-3}{2}=\frac{x+2}{3}$$

Perform the indicated operations and write the result in standard form. $$ \sqrt{-81}-\sqrt{-144} $$

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. $$ -9 x \geq 36 $$

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