Chapter 2

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}-4 x-17 \leq 4 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ -3 \leq x<5 $$

Exer. 1-50: Solve the equation. $$ 3 x^{3}-4 x^{2}-27 x+36=0 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (8+2 i)(7-3 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 48 x^{2}+12 x-90=0 $$

Solve the equation. $$0.3(3+2 x)+1.2 x=3.2$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x(2 x+3) \geq 5 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ 3 \leq x \leq 7 $$

Exer. 1-50: Solve the equation. $$ 4 x^{4}+10 x^{3}=6 x^{2}+15 x $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (5-2 i)^{2} $$

Exer. 1-14: Solve the equation by factoring. $$ 12 x^{2}+60 x+75=0 $$

A city government has approved the construction of an \(\$ 800\) million sports arena. Up to \(\$ 480\) million will be raised by selling bonds that pay simple interest at a rate of \(6 \%\) annually. The remaining amount (up to \(\$ 640\) million) will be obtained by borrowing money from an insurance company at a simple interest rate of \(5 \%\). Determine whether the arena can be financed so that the annual interest is \(\$ 42\) million.

Solve the equation. $$1.5 x-0.7=0.4(3-5 x)$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x(3 x-1) \leq 4 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ -3

Exer. 1-50: Solve the equation. $$ 15 x^{5}-20 x^{4}=6 x^{3}-8 x^{2} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (6+7 i)^{2} $$

Exer. 1-14: Solve the equation by factoring. $$ 4 x^{2}-72 x+324=0 $$

Six hundred people attended the premiere of a motion picture. Adult tickets cost \(\$ 9\), and children were admitted for \(\$ 6\). If box office receipts totaled \(\$ 4800\), how many children attended the premiere?

Solve the equation. $$\frac{3+5 x}{5}=\frac{4-x}{7}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 6 x-8>x^{2} $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ 5>x \geq-2 $$

Exer. 1-50: Solve the equation. $$ y^{3 / 2}=5 y $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ i(3+4 i)^{2} $$

Exer. 1-14: Solve the equation by factoring. $$ \frac{2 x}{x+3}+\frac{5}{x}-4=\frac{18}{x^{2}+3 x} $$

A consulting engineer's time is billed at \(\$ 60\) per hour, and her assistant's is billed at \(\$ 20\) per hour. A customer received a bill for \(\$ 580\) for a certain job. If the assistant worked 5 hours less than the engineer, how much time did each bill on the job?

Solve the equation. $$\frac{2 x-9}{4}=2+\frac{x}{12}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x+12 \leq x^{2} $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ -3 \geq x>-5 $$

Exer. 1-50: Solve the equation. $$ y^{4 / 3}=-3 y $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ i(2-7 i)^{2} $$

Exer. 1-14: Solve the equation by factoring. $$ \frac{5 x}{x-2}+\frac{3}{x}+2=\frac{-6}{x^{2}-2 x} $$

In a certain medical test designed to measure carbohydrate tolerance, an adult drinks 7 ounces of a \(30 \%\) glucose solution. When the test is administered to a child, the glucose concentration must be decreased to \(20 \%\). How much \(30 \%\) glucose solution and how much water should be used to prepare 7 ounces of \(20 \%\) glucose solution?

Solve the equation. $$\frac{13+2 x}{4 x+1}=\frac{3}{4}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}<16 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ (-5,8] $$

Exer. 1-50: Solve the equation. $$ \sqrt{7-5 x}=8 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (3+4 i)(3-4 i) $$

Exer. 1-14: Solve the equation by factoring. $$ \frac{5 x}{x-3}+\frac{4}{x+3}=\frac{90}{x^{2}-9} $$

A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a \(2 \%\) active ingredient, but the pharmacist only has \(10 \%\) solution and \(1 \%\) solution in stock. How much of each type of solution should be used to fill the prescription?

Solve the equation. $$\frac{3}{7 x-2}=\frac{9}{3 x+1}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}>9 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ [0,4) $$

Exer. 1-50: Solve the equation. $$ \sqrt{2 x-9}=\frac{1}{3} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (4+9 i)(4-9 i) $$

British sterling silver is a copper-silver alloy that is \(7.5 \%\) copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 200 grams of a copper-silver alloy that is \(10 \%\) copper by weight?

Solve the equation. $$8-\frac{5}{x}=2+\frac{3}{x}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 25 x^{2}-9<0 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ [-4,-1] $$

Exer. 1-50: Solve the equation. $$ 2+\sqrt[3]{1-5 t}=0 $$