Video: Solving Linear Equations Involving Absolute Values

Solve |𝑥| + 12 = 18.

01:10

Video Transcript

Solve the absolute value of 𝑥 plus 12 equals 18.

In order to solve an absolute value equation, we’ll need to consider two cases. Case one is positive 𝑥 plus 12 equals 18. And case two is negative 𝑥 plus 12 equals 18. On the left side, to isolate 𝑥, we’ll subtract 12 from both sides of the equation. 12 minus 12 equals zero. 𝑥 equals 18 minus 12, which is six.

From there, we consider the negative case. First, we subtract 12 from either side. We’re left with negative 𝑥 is equal to six. If we multiply both sides of the equation by negative one, negative one times negative 𝑥 equals 𝑥. And negative one times six equals negative six. To make this equation true, 𝑥 is equal to six or negative six.

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