Chapter 2

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

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

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

Solve the quadratic equation by factoring. $$ 4 x^{2}=9 $$

For the following exercises, use this scenario: A wiress carrier offers the following plans that a person is considering. The Family Plan: s90 monthly fee, unlimited talk and text on up to 5 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 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. $$ 3 x^{3}-6 x^{2}-27 x+54=0 $$

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, plot the complex numbers on the complex plane. $$ -3-4 i $$

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

Solve the quadratic equation by factoring. $$ 2 x^{2}+14 x=36 $$

For the following exercises, use this scenario: A wiress carrier offers the following plans that a person is considering. The Family Plan: s90 monthly fee, unlimited talk and text on up to 5 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 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. $$ 4 y^{3}-9 y=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |x+9| \geq-6 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (3+2 i)+(5-3 i) $$

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

Solve the quadratic equation by factoring. $$ 5 x^{2}=5 x+30 $$

For the following exercises, use this scenario: A wiress carrier offers the following plans that a person is considering. The Family Plan: s90 monthly fee, unlimited talk and text on up to 5 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. Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.

For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$5 y+4=10 x$$

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |2 x+3| < 7 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ x^{3}+3 x^{2}-25 x-75=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |2 x+3|<7 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-2-4 i)+(1+6 i) $$

For the following exercises, solve each rational equation for \(x\). State all \(x\) -values that are excluded from the solution set. $$ \frac{3}{x}-\frac{1}{3}=\frac{1}{6} $$

Solve the quadratic equation by factoring. $$ 4 x^{2}=5 x $$

For the following exercises, use this scenario: A wiress carrier offers the following plans that a person is considering. The Family Plan: s90 monthly fee, unlimited talk and text on up to 5 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. If a family has 3 smart phones, which plan should they choose?

For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$5 x+2 y=0$$

Solve each rational equation for x. State all x-values that are excluded from the solution set. \(\frac{3}{x}-\frac{1}{3}=\frac{1}{6}\)

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |3 x-1|>11 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ m^{3}+m^{2}-m-1=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |3 x-1|>11 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-5+3 i)-(6-i) $$

For the following exercises, solve each rational equation for \(x\). State all \(x\) -values that are excluded from the solution set. $$ 2-\frac{3}{x+4}=\frac{x+2}{x+4} $$

Solve the quadratic equation by factoring. $$ 7 x^{2}+3 x=0 $$

For exercises 17 and 18, use this scenario: A retired woman has \(\$ 50,000\) to invest but needs to make \(\$ 6,000\) a year from the interest to meet certain living expenses. One bond investment pays 15\(\%\) annual interest. The rest of it she wants to put in a CD that pays 7\(\% .\) If we let \(x\) be the amount the woman invests in the 15\(\%\) bond, how much will she be able to invest in the CD?

For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. $$(-4,1) \text { and }(3,-4)$$

Solve each rational equation for x. State all x-values that are excluded from the solution set. \(2-\frac{3}{x+4}=\frac{x+2}{x+4}\)

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |2 x+1|+1 \leq 6 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ 2 x^{3}-14 x^{3}=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |2 x+1|+1 \leq 6 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (2-3 i)-(3+2 i) $$

For the following exercises, solve each rational equation for \(x\). State all \(x\) -values that are excluded from the solution set. $$ \frac{3}{x-2}=\frac{1}{x-1}+\frac{7}{(x-1)(x-2)} $$

Solve the quadratic equation by factoring. $$ \frac{x}{3}-\frac{9}{x}=2 $$

For exercises 17 and 18, use this scenario: A retired woman has \(\$ 50,000\) to invest but needs to make \(\$ 6,000\) a year from the interest to meet certain living expenses. One bond investment pays 15\(\%\) annual interest. The rest of it she wants to put in a CD that pays 7\(\% .\) Set up and solve the equation for how much the woman should invest in each option to sustain a \(\$ 6,000\) annual return.

For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. $$(2,-5) \text { and }(7,4)$$

Solve each rational equation for x. State all x-values that are excluded from the solution set. \(\frac{3}{x-2}=\frac{1}{x-1}+\frac{7}{(x-1)(x-2)}\)