Chapter 1

Determine whether each value of \(x\) is a solution of the inequality. \(0<\frac{x-2}{4}<2\) (a) \(x=4\) (b) \(x=10\) (c) \(x=0\) (d) \(x=\frac{7}{2}\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(4 x^{4}-65 x^{2}+16=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ x^{2}+8 x-4=0 $$

Solve the quadratic equation by factoring. $$ 3+5 x-2 x^{2}=0 $$

In Exercises 17-22, write a mathematical model for the number problem, and solve the problem. Find two consecutive numbers whose sum is 525 .

In Exercises 17-54, solve the equation and check your solution. (Some equations have no solution.) $$ x+10=15 $$

In Exercises 7-16, determine whether each value of \(x\) is a solution of the equation. Equation $$ 5 x-3=3 x+5 $$ Values (a) \(x=0\) (b) \(x=-5\) (c) \(x=4\) (d) \(x=10\)

Solve the inequality. Then graph the solution set on the real number line. \(6(x+2)(x-1)<0\)

Determine whether each value of \(x\) is a solution of the inequality. \(-1<\frac{3-x}{2} \leq 1\) (a) \(x=0\) (b) \(x=-5\) (c) \(x=1\) (d) \(x=5\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(36 t^{4}+29 t^{2}-7=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 4 x^{2}-4 x-4=0 $$

Solve the quadratic equation by factoring. $$ 2 x^{2}=19 x+33 $$

Write a mathematical model for the number problem, and solve the problem. Find three consecutive natural numbers whose sum is 804 .

Solve the equation and check your solution. (Some equations have no solution.) $$ 9-x=13 $$

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

Determine whether each value of \(x\) is a solution of the inequality. \(|x-10| \geq 3\) (a) \(x=13\) (b) \(x=-1\) (c) \(x=14\) (d) \(x=9\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(x^{6}+7 x^{3}-8=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 12 x-9 x^{2}=-3 $$

Solve the quadratic equation by factoring. $$ x^{2}+4 x=12 $$

Write a mathematical model for the number problem, and solve the problem. One positive number is five times another positive number. The difference between the two numbers is 148 . Find the numbers.

Solve the equation and check your solution. (Some equations have no solution.) $$ 7-2 x=15 $$

Solve the inequality. Then graph the solution set on the real number line. \(x^{2}-4 x-1>0\)

Determine whether each value of \(x\) is a solution of the inequality. \(|3 x+5|>7\) (a) \(x=-5\) (b) \(x=-2\) (c) \(x=\frac{1}{3}\) (d) \(x=10\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(x^{6}+3 x^{3}+2=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 16 x^{2}+22=40 x $$

Solve the quadratic equation by factoring. $$ x^{2}+4 x=21 $$

Write a mathematical model for the number problem, and solve the problem. One positive number is one-fifth of another number. The difference between the two numbers is 76 . Find the numbers.

Solve the equation and check your solution. (Some equations have no solution.) $$ 7 x+2=16 $$

Solve the inequality. Then graph the solution set on the real number line. \(4 x^{3}-6 x^{2}<0\)

Determine whether each value of \(x\) is a solution of the inequality. \(|x+2| \leq 10\) (a) \(x=-15\) (b) \(x=-4\) (c) \(x=1\) (d) \(x=8\)

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt{2 x}-10=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 36 x^{2}+24 x=7 $$

Solve the quadratic equation by factoring. $$ -x^{2}-7 x=10 $$

Write a mathematical model for the number problem, and solve the problem. Find two consecutive integers whose product is five less than the square of the smaller number.

Solve the equation and check your solution. (Some equations have no solution.) $$ 8 x-5=3 x+10 $$

Solve the inequality. Then graph the solution set on the real number line. \(4 x^{3}-12 x^{2}>0\)

Determine whether each value of \(x\) is a solution of the inequality. \(|2 x-3|<15\) (a) \(x=-6\) (b) \(x=0\) (c) \(x=12\) (d) \(x=7\)

Find the real solution(s) of the radical equation. Check your solutions. \(4 \sqrt{x}-3=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 3 x+x^{2}-1=0 $$

Solve the quadratic equation by factoring. $$ -x^{2}+8 x=12 $$

Write a mathematical model for the number problem, and solve the problem. Find two consecutive natural numbers such that the difference of their reciprocals is one-fourth the reciprocal of the smaller number.

Solve the equation and check your solution. (Some equations have no solution.) $$ 7 x+3=3 x-13 $$

Solve the inequality. Then graph the solution set on the real number line. \(x^{3}-4 x \geq 0\)

Copy and complete the statement using the correct inequality symbol. If \(2 x>6\), then \(x \longrightarrow 3\)

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt{x-10}-4=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 4 x^{2}+4 x=7 $$

In Exercises 23-40, solve the quadratic equation by extracting square roots. List both the exact answer and a decimal answer that has been rounded to two decimal places. $$ x^{2}=16 $$

Your weekly paycheck is \(12 \%\) more than your coworker's. Your two paychecks total \(\$ 848\). Find the amount of each paycheck.

Solve the equation and check your solution. (Some equations have no solution.) $$ 2(x+5)-7=3(x-2) $$

Solve the inequality. Then graph the solution set on the real number line. \(2 x^{3}-x^{4} \leq 0\)