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Chapter 1: Q39. (page 37)

PART-TIME JOB

David earns \(5.60 an hour working at Box Office Videos. Each week, 25% of his total pay is deducted for taxes. If David wants his take-home pay to be at least \)105 a week, solve the inequality 5.6x-0.255.6x鈮�105 to determine how many hours he must work.

Short Answer

Expert verified

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 by step solution

01

- Write properties of inequality

Properties of inequalities are written in following table:

02

- Simplify left side of 5.6x-0.255.6x≥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=a+bc

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

5.6x鈭�0.255.6x鈮�1055.6鈭�0.255.6x鈮�1055.6鈭�1.4x鈮�1054.2x鈮�105

03

- Simplify 4.2x≥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

4.2x鈮�1054.2x4.2鈮�1054.2x鈮�25

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

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