Chapter 2

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. $$ 5 x^{3}+45 x=2 x^{2}+18 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |x-2|+4 \geq 10 $$

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. $$ \frac{3 x}{x-1}+2=\frac{3}{x-1} $$

Solve the quadratic equation by using the square root property. $$ x^{2}=36 $$

Two planes fly in opposite directions. One travels 450 \(\mathrm{mi} / \mathrm{h}\) and the other \(550 \mathrm{mi} / \mathrm{h}\). How long will it take before they are \(4,000 \mathrm{mi}\) apart?

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. $$(5,0)\text { and }(5,6)$$

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

Solve the quadratic equation by using the square root property. $$ x^{2}=49 $$

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?

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?

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 radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{x-7}=5 $$

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

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

Fiora starts riding her bike at 20 \(\mathrm{mi}\) 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 \(\mathrm{mi} / \mathrm{h} ?\)

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

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. \((19,12)\) and \((41,71)\)

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 \(20 \mathrm{mi} / \mathrm{h}\) ?

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

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

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

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |x-20|>-1 $$

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 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. $$ (0,3) \text { with a slope of } \frac{2}{3} $$

Solve the quadratic equation by using the square root property. $$ (x-3)^{2}=7 $$

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

A chemistry teacher needs to mix a \(30 \%\) salt solution with a \(70 \%\) salt solution to make 20 qt of a \(40 \%\) salt solution. How many quarts of each solution should the teacher mix to get the desired result?

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. $$ \sqrt{3 t+5}=7 $$

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

Find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. \((1,2)\) with a slope of \(-\frac{4}{5}\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-2+4 i)(8) $$

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. $$ (1,2) \text { with a slope of }-\frac{4}{5} $$

Paul has \(\$ 20,000\) to invest. His intent is to earn \(11 \%\) interest on his investment. He can invest part of his money at \(8 \%\) interest and part at \(12 \%\) interest. How much does Paul need to invest in each option to make get a total \(11 \%\) return on his \(\$ 20,000 ?\)

Solve the quadratic equation by using the square root property. $$ (2 x+1)^{2}=9 $$

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. $$(-1,1)\text { and }(7,-4)$$

For the following exercises, describe all the \(x\) -values within or including a distance of the given values. Distance of 5 units from the number 7

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{t+1}+9=7 $$

Find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. \(x\) -intercept is \(1,\) and \((-2,6)\)

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, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. $$ x \text { -intercept is } 1, \text { and }(-2,6) $$