Chapter 1

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Nine times a number is 30 more than three times that number. Find the number.

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ 20-\frac{x}{3}=\frac{x}{2} $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(5-2 i)^{2}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 4 x^{2}+1 \geq 4 x $$

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

Solve each radical equation in Check all proposed solutions. $$ \sqrt{3 x}+10=x+4 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$(x-3)^{2}=36$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(3, \infty)$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Five more than four times a number is that number increased by \(35 .\) Find the number.

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{5}-\frac{1}{2}=\frac{x}{6} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{2}{3-i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x \geq 0 $$

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

Solve each radical equation in Check all proposed solutions. $$ \sqrt{x+8}-\sqrt{x-4}=2 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$(3 x+2)^{2}=9$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-3, \infty)$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{3 x}{5}=\frac{2 x}{3}+1 $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{3}{4+i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+2 x<0 $$

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

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

Solve each equation in Exercises \(15-26\) by the square root method. $$(4 x-1)^{2}=16$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-5, \infty)$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{2}=\frac{3 x}{4}+5 $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{2 i}{1+i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 2 x^{2}+3 x>0 $$

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 Check all proposed solutions. $$ \sqrt{x+5}-\sqrt{x-3}=2 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$(5 x-1)^{2}=7$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(-\infty, 3)$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{3 x}{5}-x=\frac{x}{10}-\frac{5}{2} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{5 i}{2-i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}-5 x \leq 0 $$

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 Check all proposed solutions. $$ \sqrt{2 x-3}-\sqrt{x-2}=1 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$(8 x-3)^{2}=5$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(-\infty, 2)$$

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ 2 x-\frac{2 x}{7}=\frac{x}{2}+\frac{17}{2} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{8 i}{4-3 i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ -x^{2}+x=0 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=4-x^{2}$$

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

Solve each equation in Exercises \(15-26\) by the square root method. $$(3 x-4)^{2}=8$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(-\infty, 5.5)$$

The formula $$ \frac{W}{2}-3 H=53 $$ models the recommended weight \(W\), in pounds, for a male, where \(H\) represents the man's height, in inches, over 5 feet. What is the recommended weight for a man who is 6 feet, 3 inches tall?

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x+3}{6}=\frac{3}{8}+\frac{x-5}{4} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{-6 i}{3+2 i}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ -x^{2}+2 x \geq 0 $$

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 Check all proposed solutions. $$ \sqrt{2 x+3}+\sqrt{x-2}=2 $$