Chapter 1

Solve the equation and check your solution. (Some equations have no solution.) $$ 3=2+\frac{2}{z+2} $$

Solve the inequality and write the solution set in interval notation. \(6 x^{3}-10 x^{2}>0\)

Solve the inequality. Then graph the solution set on the real number line. \(-4<\frac{2 x-3}{3}<4$$-4<\frac{2 x-3}{3}<4\)

Find the real solution(s) of the equation involving absolute value. Check your solutions. \(|x+1|=2\)

Writing Real-Life Problems In Exercises 47-50, solve the number problem and write a real-life problem that could be represented by this verbal model. For instance, an applied problem that could be represented by Exercise 47 is as follows. The sum of the length and width of a one-story house is 100 feet. The house has 2500 square feet of floor space. What are the length and width of the house? One number is 1 more than another number. The sum of their squares is \(113 .\) Find the numbers.

Solve the quadratic equation using any convenient method. \((x+4)^{2}=49\)

Course Grade To get an \(A\) in a course, you need an average of \(90 \%\) or better on four tests that are worth 100 points each. Your scores on the first three tests were 87,92 , and 84 . What must you score on the fourth test to get an A for the course?

Solve the equation and check your solution. (Some equations have no solution.) $$ (x+2)^{2}+5=(x+3)^{2} $$

Solve the inequality and write the solution set in interval notation. \(25 x^{3}-10 x^{2}<0\)

Solve the inequality. Then graph the solution set on the real number line. \(0 \leq \frac{x+3}{2}<5\)

Find the real solution(s) of the equation involving absolute value. Check your solutions. \(|x-2|=3\)

Writing Real-Life Problems In Exercises 47-50, solve the number problem and write a real-life problem that could be represented by this verbal model. For instance, an applied problem that could be represented by Exercise 47 is as follows. The sum of the length and width of a one-story house is 100 feet. The house has 2500 square feet of floor space. What are the length and width of the house? One number is 2 more than another number. The product of the two numbers is 440 . Find the numbers

Solve the quadratic equation using any convenient method. \((x-3)^{2}=36\)

Course Grade To get an \(\mathrm{A}\) in a course, you need an average of \(90 \%\) or better on four tests. The first three tests are worth 100 points each and the fourth is worth 200 points. Your scores on the first three tests are 87,92, and 84\. What must you score on the fourth test to get an A for the course?

Solve the equation and check your solution. (Some equations have no solution.) $$ (x+1)^{2}+2(x-2)=(x+1)(x-2) $$

Solve the inequality and write the solution set in interval notation. \(x^{3}-9 x \leq 0\)

Solve the inequality. Then graph the solution set on the real number line. \(\frac{3}{4}>x+1>\frac{1}{4}\)

Find the real solution(s) of the equation involving absolute value. Check your solutions. \(|2 x-1|=5\)

Use the cost equation to find the number of units \(x\) that a manufacturer can produce for the cost \(C\). (Round your answer to the nearest positive integer.) \(C=0.125 x^{2}+20 x+5000 \quad C=\$ 14,000\)

Solve the quadratic equation using any convenient method. \(4 x=4 x^{2}-3\)

The price of a swimming pool has been discounted \(15 \%\). The sale price is \(\$ 1200\). Find the original list price of the swimming pool.

Solve the equation and check your solution. (Some equations have no solution.) $$ (x+2)^{2}-x^{2}=4(x+1) $$

Solve the inequality and write the solution set in interval notation. \(4 x^{3}-x^{4} \geq 0\)

Solve the inequality. Then graph the solution set on the real number line. \(-1<-\frac{x}{3}<1\)

Find the real solution(s) of the equation involving absolute value. Check your solutions. \(|3 x+2|=7\)

Use the cost equation to find the number of units \(x\) that a manufacturer can produce for the cost \(C\). (Round your answer to the nearest positive integer.) \(C=0.5 x^{2}+15 x+5000 \quad C=\$ 11,500\)

Solve the quadratic equation using any convenient method. \(80+6 x=9 x^{2}\)

List Price The price of a home theater system has been discounted \(10 \%\). The sale price is \(\$ 499\). Find the original price of the system.

Solve the equation and check your solution. (Some equations have no solution.) $$ 4(x+1)-3 x=x+5 $$

Solve the inequality and write the solution set in interval notation. \((x-1)^{2}(x+2)^{3} \geq 0\)

Solve the inequality. Then graph the solution set on the real number line. \(|x|<6\)

Use the cost equation to find the number of units \(x\) that a manufacturer can produce for the cost \(C\). (Round your answer to the nearest positive integer.) \(C=800+0.04 x+0.002 x^{2} \quad C=\$ 1680\)

Solve the quadratic equation using any convenient method. \(50+5 x=3 x^{2}\)

Discount Rate A satellite radio system for your car has been discounted by \(\$ 30\). The sale price is \(\$ 119\). What percent of the original list price is the discount?

Solve the equation and check your solution. (Some equations have no solution.) $$ (2 x+1)^{2}=4\left(x^{2}+x+1\right) $$

Solve the inequality and write the solution set in interval notation. \(x^{4}(x-3) \leq 0\)

Solve the inequality. Then graph the solution set on the real number line. \(|x|>8\)

Find the real solution(s) of the equation involving absolute value. Check your solutions. \(\left|x^{2}+6 x\right|=3 x+18\)

Use the cost equation to find the number of units \(x\) that a manufacturer can produce for the cost \(C\). (Round your answer to the nearest positive integer.) \(C=312.5-10 x+0.4 x^{2} \quad C=\$ 900\)

Solve the quadratic equation using any convenient method. \(144-73 x+4 x^{2}=0\)

Discount Rate The price of a shirt has been discounted by \(\$ 20\). The sale price is \(\$ 29.95\). What percent of the original list price is the discount?

Solve the equation and check your solution. (Some equations have no solution.) $$ (2 x-1)^{2}=4\left(x^{2}-x+6\right) $$

Use a calculator to solve the inequality. (Round each number in your answer to two decimal places.) \(0.4 x^{2}+5.26<10.2\)

Solve the inequality. Then graph the solution set on the real number line. \(\left|\frac{x}{2}\right|>3\)

A rectangular classroom seats 72 students. If the seats were rearranged with three more seats in each row, the classroom would have two fewer rows. Find the original number of seats in each row.

Solve the quadratic equation using any convenient method. \(12 x=x^{2}+27\)

Wholesale Price A store marks up a power drill \(60 \%\) from its wholesale price. In a clearance sale, the price is discounted by \(25 \%\). The sale price is \(\$ 21.60\). What was the wholesale price of the power drill?

A student states that the solution to the equation \(\frac{2}{x(x-2)}+\frac{5}{x}=\frac{1}{x-2}\) is \(x=2\). Describe and correct the student's error.

Use a calculator to solve the inequality. (Round each number in your answer to two decimal places.) \(-1.3 x^{2}+3.78>2.12\)

Solve the inequality. Then graph the solution set on the real number line. \(|5 x|>10\)