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In $15-26,$ solve each inequality and write the solution set if the variable is an element of the set of integers.$$|y+2|>7$$

$x \in(-\infty,-9) \cup(5, \infty)$

Algebra

Chapter 1

THE INTEGERS

Section 4

Solving Absolute Value Equations and Inequalities

The Integers

Equations and Inequalities

Polynomials

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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In $15-26,$ solve each ine…

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In $15-26,$ find and graph…

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all right, We're asked to solve the absolute value inequality here, and we can do that by breaking it up into two separate equations. So the first equation makes sense, because if y plus two is greater than seven than the absolute value of Y, plus two is greater than seven. But also, if why plus two happens to be less than negative seven in the absolute value of Y, plus two will then be greater than seven as well. So this is how you're gonna flip, do your inequalities. And so on the left side, you can subtract two from both sides. Why is greater than five? And on the right side you can get you could subtract two from both sides and get why less than negative nine. And so the best way to write out the solutions if you want to get a more comprehensive idea, is to draw a number line, and we will include the integers zero and one two. Anything doesn't That's a one. Then over here you have minus one minus two minus three minus for Carly contained this mother out minus five, minus six minus seven. And basically what they're saying is this inequality is true. Whenever we use an open circle to tell you that minus seven isn't included This inequality is true. When why is over here? And it's also true. One why is over here? So they're infinitely many integers that satisfy this. And if I was going to write that in some sort of sanitation, I would write that as the scent of why such that why is greater than five, or why is less than negative tonight, which is a mistake I made over here. This should be minus nine. And so there's a pictorial representation of your solution. And so everything in here isn't No, it wouldn't work. But if you plug in anything bigger than five or less than minus nine, this absolute value inequality holds. And so this would be a set representation. And so they're infinitely many managers in this solution.

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