Equations Involving Absolute Value

To solve an equation containing $|\cdot|$, isolate the absolute value on one side, then split into the two cases from §2.3.1: $|u|=r$ (with $r\ge0$) becomes $u=r$ or $u=-r$.

Worked pattern. For $|2x-17|=3$: split into $2x-17=3$ or $2x-17=-3$, giving $x=10$ or $x=7$.

With an outer coefficient. For $3|x-2|+7=19$: first isolate the absolute value, $|x-2|=\dfrac{19-7}3=4$, then split: $x-2=4$ or $x-2=-4$, giving $x=6$ or $x=-2$. …