Chapter 1

Copy and complete the statement using the correct inequality symbol. If \(3 x>9\), then \(x\) \(?_____ 3 .\)

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt{5-x}-3=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 16 x^{2}-40 x+5=0 $$

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. $$ x^{2}=144 $$

Your weekly paycheck is \(12 \%\) less 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.) $$ 2(13 t-15)+3(t-19)=0 $$

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

Copy and complete the statement using the correct inequality symbol. If \(2 x \leq-8\), then \(x\) ________\(-4\).

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt[3]{2 x+5}+3=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 28 x-49 x^{2}=4 $$

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. $$ x^{2}=7 $$

The profit for a company in February was \(5 \%\) higher than it was in January. The total profit for the two months was \(\$ 129,000\). Find the profit for each month.

Solve the equation and check your solution. (Some equations have no solution.) $$ 6[x-(2 x+3)]=8-5 x $$

Solve the inequality. Then graph the solution set on the real number line. \(x^{3}+5 x^{2}-4 x-20 \leq 0\)

Copy and complete the statement using the correct inequality symbol. If \(3 x \leq-15\), then \(x\) ______\(-5\).

Find the real solution(s) of the radical equation. Check your solutions. \(\sqrt[3]{3 x+1}-5=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 9 x^{2}+24 x+16=0 $$

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. $$ x^{2}=27 $$

The profit for a company in February was \(5 \%\) lower than it was in January. The total profit for the two months was \(\$ 129,000\). Find the profit for each month.

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

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

Copy and complete the statement using the correct inequality symbol. If \(2-4 x>-10\), then \(x\)______3.

Find the real solution(s) of the radical equation. Check your solutions. \(2 x+9 \sqrt{x}-5=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 8 t=5+2 t^{2} $$

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. $$ 3 x^{2}=36 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{5 x}{4}+\frac{1}{2}=x-\frac{1}{2} $$

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

Copy and complete the statement using the correct inequality symbol. If \(5-3 x>-7\), then \(x\) _______4.

Find the real solution(s) of the radical equation. Check your solutions. \(6 x-7 \sqrt{x}-3=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ 25 h^{2}+80 h+61=0 $$

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. $$ 9 x^{2}=25 $$

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

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

Copy and complete the statement using the correct inequality symbol. If \(-\frac{2}{3} x \geq-6\), then \(x\)_______ \(9 .\)

Find the real solution(s) of the radical equation. Check your solutions. \(x=\sqrt{11 x-30}\)

Use the Quadratic Formula to solve the quadratic equation. $$ (y-5)^{2}=2 y $$

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. $$ (x-12)^{2}=18 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{3}{2}(z+5)-\frac{1}{4}(z+24)=0 $$

Solve the inequality. Then graph the solution set on the real number line. \(\frac{x+12}{x+2} \geq 3\)

Copy and complete the statement using the correct inequality symbol. If \(-\frac{3}{4} x \geq-12\), then \(x\)_________16.

Find the real solution(s) of the radical equation. Check your solutions. \(2 x-\sqrt{15-4 x}=0\)

Use the Quadratic Formula to solve the quadratic equation. $$ (x+6)^{2}=-2 x $$

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. $$ (x+13)^{2}=21 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ \frac{3 x}{2}+\frac{1}{4}(x-2)=10 $$

Solve the inequality. Then graph the solution set on the real number line. \(\frac{3}{2} x \geq 9\)

Find the real solution(s) of the radical equation. Check your solutions. \(-\sqrt{26-11 x}+4=x\)

In Exercises 31-36, use a calculator to solve the quadratic equation. (Round your answer to three decimal places.) $$ 5.1 x^{2}-1.7 x-3.2=0 $$

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. $$ (x+2)^{2}=12 $$

Solve the equation and check your solution. (Some equations have no solution.) $$ 0.25 x+0.75(10-x)=3 $$

Solve the inequality. Then graph the solution set on the real number line. \(\frac{2}{5} x>7\)