Help with absolute value inequalities?

Question

I tried to solve this problem. According to the book, the answer is all real numbers. But I'm not getting that answer when I try to work out the problem. What am I doing wrong? Thanks.


| 2y - 9 | > -5

2y - 9 > -5 or -2y + 9 < 5
2y > 4 -2y < -4
2y/2 > 4/2 -2y/-2 < -4/-2
y > 2 y < 2

Answer 1

Where you went wrong was losing the absolute value bars when you started working with the inequality.

Absolute value refers to the distance from zero on a number line, and by definition it can't be a negative number.

Soooo ... anything between the bars will end up being zero or a positive number, no matter what you plug in for y. And that will always be greater than -5. And there's the answer!

Answer 2

Absolute value Inequalities.

∣2y - 9∣> - 5

2y - 9 > - 5

2y - 9 + 9 > - 5 + 9

2y > 4

2y/2 > 4/2

y > 4/2

y > 2

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Check the following Link. locate ∣2x - 3 ∣ > 5. it will explain a step by step procedure for solving absolute values inequalities.

www.purplemath.com/modules/absineq.htm


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