91Ó°ÊÓ

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 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 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. $$ \sqrt{3 x-1}-2=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |-2 x+7| \leq 13 $$

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

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. $$(-4,3)\text { and }(10,3)$$

Ben starts walking along a path at \(4 \mathrm{mi} / \mathrm{h} .\) One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at \(6 \mathrm{mi} / \mathrm{h}\). How long will it be before Amanda catches up to Ben?

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\(\% .\) Ben starts walking along a path at 4 \(\mathrm{mi} / \mathrm{h}\) . One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 6 \(\mathrm{mi} / \mathrm{h}\) . How long will it be before Amanda catches up to Ben?

Solve the quadratic equation by using the square root property. $$ (x-1)^{2}=25 $$