Chapter 1

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

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

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.

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

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

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

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

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.

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

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

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

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

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

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

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?

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

Perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-8}+3 \sqrt{-18} $$

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

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

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

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

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

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

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

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

Perform the indicated operations and write the result in standard form. $$ (-5-\sqrt{-9})^{2} $$

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

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

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. $$ \frac{2}{3 x}+\frac{1}{4}-\frac{11}{6 x}-\frac{1}{3} $$

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

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

Solve each equation with rational exponents. Check all proposed solutions. $$6 x^{\frac{5}{2}}-12-0$$

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

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

Perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-11})^{2} $$

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

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

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

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. 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?

Perform the indicated operations and write the result in standard form. $$ \frac{-8+\sqrt{-32}}{24} $$

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

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. 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?

Perform the indicated operations and write the result in standard form. $$ \frac{-12+\sqrt{-28}}{32} $$

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

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

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. $$ \frac{1}{x-1}+5-\frac{11}{x-1} $$

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 \(\$ 7000\) 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?

Perform the indicated operations and write the result in standard form. $$ \frac{-6-\sqrt{-12}}{48} $$

Solve each equation with rational exponents. Check all proposed solutions. $$\left(x^{2}-x-4\right)^{\frac{3}{4}}-2-6$$

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