Absolute value equation

Solve the absolute value equation $|x - 2| = 3$ by reading it as the intersection of $y = |x - 2|$ and $y = 3$. Since $|x - 2| = 3$ means $x - 2 = 3$ or $x - 2 = -3$, the solutions are $x = 5$ and $x = -1$.

The two intersection points are therefore $(5, 3)$ and $(-1, 3)$, marked by the large dots. Because $y = |x - 2|$ is a V-shape with its corner at $x = 2$, it meets the horizontal line $y = 3$ at two points.