Chapter 2

For the following exercises, solve the quadratic equation by factoring. $$ 2 x^{2}+9 x-5=0 $$

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

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?

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

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. $$ (x-1)^{\frac{3}{4}}=8 $$

For the following exercises, solve the quadratic equation by factoring. $$ 6 x^{2}+17 x+5=0 $$

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

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 $$\$ .05 /$$ min for calls. Company \(B\) has a monthly fee of $$\$ 5$$ and charges $$\$ .10 / \mathrm{min}$$ for calls. Find the model of the total cost of Company A's plan, using \(m\) for the minutes.

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

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. $$ (x+1)^{\frac{2}{3}}=4 $$

For the following exercises, solve the quadratic equation by factoring. $$ 4 x^{2}-12 x+8=0 $$

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, 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 $$\$ .05 /$$ min for calls. Company \(B\) 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 the following exercises, solve the equation for \(x\). $$ \frac{1}{2}-\frac{1}{3} x=\frac{4}{3} $$

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. $$ x^{\frac{2}{3}}-5 x^{\frac{1}{3}}+6=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 3 x^{2}-75=0 $$

For the following exercises, plot the complex numbers on the complex plane. \(1-2 i\)

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 $$\$ .05 /$$ min for calls. Company \(B\) 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 the following exercises, solve the equation for \(x\). $$ \frac{x}{3}-\frac{3}{4}=\frac{2 x+3}{12} $$

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. $$ x^{\frac{7}{3}}-3 x^{\frac{4}{3}}-4 x^{\frac{1}{3}}=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 8 x^{2}+6 x-9=0 $$

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

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 $$\$ .05 /$$ min for calls. Company \(B\) 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 the following exercises, solve the equation for \(x\). $$ \frac{2}{3} x+\frac{1}{2}=\frac{31}{6} $$

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. $$ \frac{x+3}{8}-\frac{x+5}{5} \geq \frac{3}{10} $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ x^{3}+2 x^{2}-x-2=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 4 x^{2}=9 $$

For the following exercises, plot the complex numbers on the complex plane. \(i\)

For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $$\$ 90$$ monthly fee, unlimited talk and text on up to 8 lines, and data charges of $$\$ 40$$ for each device for up to \(2 \mathrm{~GB}\) of data per device. The Mobile Share Plan: $$\$ 120$$ monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $$\$ 35$$ for each device up to a shared total of \(10 \mathrm{~GB}\) of data. Use \(P\) for the number of devices that need data plans as part of their cost. Find the model of the total cost of the Family Plan.

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

For each of the following exercises, solve the equation for y in terms of \(x\). $$ 2 x=5-3 y $$

For the following exercises, solve the inequality. Write your final answer in interval notation. $$ \frac{x-1}{3}+\frac{x+2}{5} \leq \frac{3}{5} $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ 3 x^{3}-6 x^{2}-27 x+54=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 2 x^{2}+14 x=36 $$

For the following exercises, plot the complex numbers on the complex plane. \(-3-4 i\)

For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $$\$ 90$$ monthly fee, unlimited talk and text on up to 8 lines, and data charges of $$\$ 40$$ for each device for up to \(2 \mathrm{~GB}\) of data per device. The Mobile Share Plan: $$\$ 120$$ monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $$\$ 35$$ for each device up to a shared total of \(10 \mathrm{~GB}\) of data. Use \(P\) for the number of devices that need data plans as part of their cost. Find the model of the total cost of the Mobile Share Plan.

For the following exercises, solve the equation for \(x\). $$ \frac{2 x}{3}-\frac{3}{4}=\frac{x}{6}+\frac{21}{4} $$

For each of the following exercises, solve the equation for y in terms of \(x\). $$ x-2 y=7 $$

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |x+9| \geq-6 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ 4 y^{3}-9 y=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 5 x^{2}=5 x+30 $$