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Question 304937: Suppose Erika makes at least four times as much as Gabe does, and at most, half of what John makes. Let e, g, and j be the salaries of Erika, Gabe, and John respectively. Which of the following inequalities describe this situation?
A. e 4g and e j / 2
B. 4e g and e / 2 j
C. e > 4g and e < j / 2
D. 4e > g and e / 2 < j
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Your answer should be:
4g <= e <= j/2
You start with e >= 4g which means that erika makes at least 4 times as much as gabe.
If she makes at least 4 times as much as gabe, that means that she could make exactly 4 times as much as gabe, or more than 4 times as much as gabe.
e >= 4g is the same as 4g <= e.
You just read it backwards.
Algebraically, you would determine it as follows:
You start with:
e >= 4g
You subtract e from both sides of the equation and you subtract 4g from both sides of the equation to get:
-4g >= -e
You multiply both sides of the equation by -1 to get:
4g <= e
Multiplying both sides of the equation by -1 reverses the inequality which is why it resulted in 4g <= e.
The second part of your equation is:
e <= j/2
This means that erika makes less than or equal to 1/2 john's salary.
1/2 john's salary is the same as j/2.
Less than or equal is the same as at most.
She could make exactly as much as j/2, or she can make less than that.
Put these 2 pieces together and you get:
4g <= e <= j/2
I do not understand your selections.
The closest one would be C which reads e > 4g and e < j/2.
What's missing is the equality part of that.
It should have read e >= 4g and e <= j/2
Your first two selections are missing equality and inequality signs so they are meaningless.
Check your selections again:
the correct selection will be either:
e >= 4g and e <= j/2
or:
4g <= e <= j/2
Best I can do.
Let me know if you found the correct selection.
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