Chapter 1

Use graphs to find each set. $$[2, \infty) \cap(4, \infty)$$

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

A new car worth \(\$ 24,000\) is depreciating in value by \(\$ 3000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 9000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x+3)^{2}=-16 $$

Check all proposed solutions. $$ \sqrt{x-5}-\sqrt{x-8}=3 $$

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

A new car worth \(\$ 45,000\) is depreciating in value by \(\$ 5000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 10,000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x-1)^{2}=-9 $$

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

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

You are choosing between two health clubs. Club A offers membership for a fee of \(\$ 40\) plus a monthly fee of \(\$ 25 .\) Club \(B\) offers membership for a fee of \(\$ 15\) plus a monthly fee of \(\$ 30\). After how many months will the total cost at each health club be the same? What will be the total cost for each club?

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x-3)^{2}=-5 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$5 x+11<26$$

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

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

You need to rent a rug cleaner. Company A will rent the machine you need for \(\$ 22\) plus \(\$ 6\) per hour. Company \(B\) will rent the same machine for \(\$ 28\) plus \(\$ 4\) per hour. After how many hours of use will the total amount spent at each company be the same? What will be the total amount spent at each company?

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x+2)^{2}=-7 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$2 x+5<17$$

Check all proposed solutions. $$ \sqrt{x+2}+\sqrt{3 x+7}=1 $$

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

The bus fare in a city is \(\$ 1.25 .\) People who use the bus have the option of purchasing a monthly discount pass for \(\$ 15.00 .\) With the discount pass, the fare is reduced to \(\$ 0.75\) Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ \sqrt{-64}-\sqrt{-25} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (3 x+2)^{2}=9 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$3 x-7 \geq 13$$

Check all proposed solutions. $$ \sqrt{3 \sqrt{x+1}}=\sqrt{3 x-5} $$

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

A discount pass for a bridge costs \(\$ 30\) per month. The toll for the bridge is normally \(\$ 5.00,\) but it is reduced to \(\$ 3.50\) for people who have purchased the discount pass. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ \sqrt{-81}-\sqrt{-144} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (4 x-1)^{2}=16 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x-2 \geq 14$$

Check all proposed solutions. $$ \sqrt{1+4 \sqrt{x}}=1+\sqrt{x} $$

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

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-16}+3 \sqrt{-81} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (5 x-1)^{2}=7 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$-9 x \geq 36$$

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

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. \(\frac{4}{x}=\frac{5}{2 x}+3\)

In \(2000,\) the population of Greece was \(10,600,000,\) with projections of a population decrease of \(28,000\) people per year. In the same year, the population of Belgium was \(10,200,000,\) with projections of a population decrease of \(12,000\) people per year. (Source: United Nations) According to these projections, when will the two countries have the same population? What will be the population at that time?

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-8}+3 \sqrt{-18} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (8 x-3)^{2}=5 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$-5 x \leq 30$$

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

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. \(\frac{5}{x}=\frac{10}{3 x}+4\)

After a \(20 \%\) reduction, you purchase a television for \(\$ 336\) What was the television's price before the reduction?

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-4})^{2} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (3 x-4)^{2}=8 $$