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.