Chapter 2

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ x^{\frac{3}{4}}=27 $$

Solve the inequality. Write your final answer in interval notation. $$ 3 x+2 \geq 7 x-1 $$

For the following exercises, evaluate the algebraic expressions. If \(y=x^{2}+3 x+5,\) evaluate \(y\) given \(x=2+i\)

For the following exercises, solve the equation for \(x\). $$ 4 x-3=5 $$

Solve the quadratic equation by factoring. $$ x^{2}-9 x+18=0 $$

For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Beth and Ann are joking that their combined ages equal Sam's age. If Beth is twice Ann's age and Sam is 69 yr old, what are Beth and Ann's ages?

If Bill was traveling \(v \mathrm{mi} / \mathrm{h}\), how would you represent Daemon's speed if he was traveling \(10 \mathrm{mi} / \mathrm{h}\) faster?

For each of the following exercises, find the \(x\)-intercept and the \(y\)-intercept without graphing. Write the coordinates of each intercept. $$3 x-2 y=6$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ -2 x+3>x-5 $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ 2 x^{\frac{1}{2}}-x^{\frac{1}{4}}=0 $$

Solve the inequality. Write your final answer in interval notation. $$ -2 x+3>x-5 $$

For the following exercises, solve the equation for \(x\). $$ 3(x+2)-12=5(x+1) $$

For the following exercises, evaluate the algebraic expressions. If \(y=2 x^{2}+x-3,\) evaluate \(y\) given \(x=2-3 i\)

Solve the quadratic equation by factoring. $$ 2 x^{2}+9 x-5=0 $$

For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Ben originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to \(28 .\) How many applications did each boy originally fill out?

Ben originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to 28 . How many applications did each boy originally fill out?

For each of the following exercises, find the \(x\)-intercept and the \(y\)-intercept without graphing. Write the coordinates of each intercept. $$4 x-3=2 y$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ 4(x+3) \geq 2 x-1 $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ (x-1)^{\frac{3}{4}}=8 $$

Solve the inequality. Write your final answer in interval notation. $$ 4(x+3) \geq 2 x-1 $$

For the following exercises, solve the equation for \(x\). $$ 12-5(x+3)=2 x-5 $$

For the following exercises, evaluate the algebraic expressions. If \(y=\frac{x+1}{2-x},\) evaluate \(y\) given \(x=5 i\)

Solve the quadratic equation by factoring. $$ 6 x^{2}+17 x+5=0 $$

For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of \(\$ 20\) and charges of \(\$ .05 / \mathrm{min}\) for calls. Company \(\mathrm{B}\) has a monthly fee of \(\$ 5\) and charges \(\$ .10 / \mathrm{min}\) for calls. Find the model of the total cost of Company As plan, using \(m\) for the minutes.

For each of the following exercises, find the \(x\)-intercept and the \(y\)-intercept without graphing. Write the coordinates of each intercept. $$3 x+8 y=9$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ -\frac{1}{2} x \leq-\frac{5}{4}+\frac{2}{5} x $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ (x+1)^{\frac{2}{3}}=4 $$

Solve the inequality. Write your final answer in interval notation. $$ -\frac{1}{2} x \leq-\frac{5}{4}+\frac{2}{5} x $$

For the following exercises, evaluate the algebraic expressions. If \(y=\frac{1+2 x}{x+3},\) evaluate \(y\) given \(x=4 i\)

For the following exercises, solve the equation for \(x\). $$ \frac{1}{2}-\frac{1}{3} x=\frac{4}{3} $$

Solve the quadratic equation by factoring. $$ 4 x^{2}-12 x+8=0 $$

For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of \(\$ 20\) and charges of \(\$ .05 / \mathrm{min}\) for calls. Company \(\mathrm{B}\) has a monthly fee of \(\$ 5\) and charges \(\$ .10 / \mathrm{min}\) for calls. Find the model of the total cost of Company B's plan, using \(m\) for the minutes.

For each of the following exercises, find the \(x\)-intercept and the \(y\)-intercept without graphing. Write the coordinates of each intercept. $$2 x-\frac{2}{3}=\frac{3}{4} y+3$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ -5(x-1)+3>3 x-4-4 x $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ x^{\frac{2}{3}}-5 x^{\frac{1}{3}}+6=0 $$

Solve the inequality. Write your final answer in interval notation. $$ -5(x-1)+3>3 x-4-4 x $$

For the following exercises, plot the complex numbers on the complex plane. $$ 1-2 i $$

For the following exercises, solve the equation for \(x\). $$ \frac{x}{3}-\frac{3}{4}=\frac{2 x+3}{12} $$

Solve the quadratic equation by factoring. $$ 3 x^{2}-75=0 $$

For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of \(\$ 20\) and charges of \(\$ .05 / \mathrm{min}\) for calls. Company \(\mathrm{B}\) has a monthly fee of \(\$ 5\) and charges \(\$ .10 / \mathrm{min}\) for calls. Find out how many minutes of calling would make the two plans equal.

For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$4 x+2 y=8$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ -3(2 x+1)>-2(x+4) $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ x^{\frac{7}{3}}-3 x^{\frac{4}{3}}-4 x^{\frac{1}{3}}=0 $$

Solve the inequality. Write your final answer in interval notation. $$ -3(2 x+1)>-2(x+4) $$

For the following exercises, plot the complex numbers on the complex plane. $$ -2+3 i $$

For the following exercises, solve the equation for \(x\). $$ \frac{2}{3} x+\frac{1}{2}=\frac{31}{6} $$

Solve the quadratic equation by factoring. $$ 8 x^{2}+6 x-9=0 $$

For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of \(\$ 20\) and charges of \(\$ .05 / \mathrm{min}\) for calls. Company \(\mathrm{B}\) has a monthly fee of \(\$ 5\) and charges \(\$ .10 / \mathrm{min}\) for calls. If the person makes a monthly average of 200 min of calls, which plan should for the person choose?

For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$3 x-2 y=6$$

For the following exercises, solve the inequality. Write your final answer in interval notation $$ \frac{x+3}{8}-\frac{x+5}{5} \geq \frac{3}{10} $$