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In $3-14,$ write the solution set of each equation.$$|x+8|=6$$

$x=-2,-14$

Algebra

Chapter 1

THE INTEGERS

Section 4

Solving Absolute Value Equations and Inequalities

The Integers

Equations and Inequalities

Polynomials

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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01:26

In $3-14,$ write the solut…

00:49

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00:08

Find the solution set for …

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07:04

Solve each equation. $…

00:33

whereas to solve the following absolute value in equation for sorry absolute value equation for X. And so the absolute value represents a distance of X plus eight from zero. Right? And so what you do when you have an absolute value problem like this is that you split it into two problems. A point where X plus eight equals six and X plus eight equals minus six. And basically what's happening here is that this is a good way of making sure that when you're on the number line, you're not just accounting for this distance from zero. But you're also accounting for this distance from zero, and so it's solving the one on the left. If I subtract eight from both sides again, X is equal to minus two. And on the right, If I subtract a from both sides, I get X is equal to minus 14 and in absolute value equations, it's very, very, very important that you check both of your answers. So if I plug minus two into this, I'm gonna get minus two plus A, which is six equals 26 that checks out and then over here, I'm going to have minus 14th plus eight equals six, which gives it the absolute value of negative six equal six, which also checks up. So both of our answers are good, and right now and again, the process of splitting these two and in court into two equations can introduce some a solutions that don't work.

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