Chapter 2

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, 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. Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.

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

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. $$ x^{3}+3 x^{2}-25 x-75=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 4 x^{2}=5 x $$

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. $$ \frac{3}{x}-\frac{1}{3}=\frac{1}{6} $$

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

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. $$ m^{3}+m^{2}-m-1=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ 7 x^{2}+3 x=0 $$

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

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

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) and (3,-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. $$ 2 x^{5}-14 x^{3}=0 $$

For the following exercises, solve the quadratic equation by factoring. $$ \frac{x}{3}-\frac{9}{x}=2 $$

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

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

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) and (7,4)

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |x-2|+4 \geq 10 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ 5 x^{3}+45 x=2 x^{2}+18 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ x^{2}=36 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-4+4 i)-(-6+9 i) $$

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

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. (5,0) and (5,6)

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |-2 x+7| \leq 13 $$

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{3 x-1}-2=0 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ x^{2}=49 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (2+3 i)(4 i) $$

For the following exercises, solve each rational equation for \(x .\) State all \(x\) -values that are excluded from the solution set. $$ \frac{5}{x+1}+\frac{1}{x-3}=\frac{-6}{x^{2}-2 x-3} $$

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. (-4,3) and (10,3)

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{x-7}=5 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ (x-1)^{2}=25 $$

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

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 \(7 \%\). Fiora starts riding her bike at 20 \(\mathrm{mi} / \mathrm{h}\). After a while, she slows down to \(12 \mathrm{mi} / \mathrm{h}\), and maintains that speed for the rest of the trip. The whole trip of \(70 \mathrm{mi}\) takes her \(4.5 \mathrm{~h}\). For what distance did she travel at \(20 \mathrm{mi} /\) \(\mathrm{h} ?\)

For the following exercises, solve each rational equation for \(x .\) State all \(x\) -values that are excluded from the solution set. $$ \frac{1}{x}=\frac{1}{5}+\frac{3}{2 x} $$

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. Find the distance between the two points given using your calculator, and round your answer to the nearest hundredth. $$(19,12) \text { and }(41,71)$$

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{x-1}=x-7 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ (x-3)^{2}=7 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (6-2 i)(5) $$

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. (0,3) with a slope of \(\frac{2}{3}\)

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. (-5,-6) and (4,2)

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ \left|\frac{x-3}{4}\right|<2 $$

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{3 t+5}=7 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ (2 x+1)^{2}=9 $$