Q39. - Algebra 2

Question

PART-TIME JOB

David earns $\backslash (5.60$ an hour working at Box Office Videos. Each week, $25\%$ of his total pay is deducted for taxes. If David wants his take-home pay to be at least $\backslash )105$ a week, solve the inequality $5.6x-0.25\left(5.6x\right)\ge 105$ to determine how many hours he must work. 

Step-by-Step Solution

Answer

If David wants his take-home pay to be at least $105 a week then he must work at least 25 hours per week.

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify left side of 5 . 6 x - 0 . 25 5 . 6 x ≥ 105

To simplify given inequality, first simplify left side of inequality by grouping the coefficient of variable x by using the properties of real number.

Take out x common from both terms using distributive property $ac+bc=\left(a+b\right)c$

Then to simplify bracket, first multiply from left to right and then subtract the resulting numbers

$\begin{array}{c}5.6x-0.25\left(5.6x\right)\ge 105\\ \left[5.6-0.25\left(5.6\right)\right]x\ge 105\\ \left[5.6-1.4\right]x\ge 105\\ 4.2x\ge 105\end{array}$

Step 3 - Simplify 4.2 x ≥ 105

To simplify, use division property of inequalities. Divide both sides by same positive number does not reverse the sign of inequality as shown below

 $\begin{array}{c}4.2x\ge 105\\ \frac{4.2x}{4.2}\ge \frac{105}{4.2}\\ x\ge 25\end{array}$

Thus, David need to work at least 25 hours per week.