Solve |2x + 1| > 3: Absolute Value Inequality Step-by-Step

The absolute value $|2x + 1|$ measures distance from zero. When this distance is greater than 3, the expression inside could be either greater than 3 or less than -3.

For 'greater than' inequalities like $|expression| > 3$, use OR because you want values that satisfy either case. For 'less than' inequalities, use AND.

Since our original inequality uses $>$ (not ≥), the boundary points where $|2x + 1| = 3$ are not included. That's why we use $x < -2$ and $x > 1$, not ≤ or ≥.

Draw a number line! Mark points at x = -2 and x = 1 with open circles (not included). Shade everything to the left of -2 and everything to the right of 1.

Absolutely! Try $x = -3$: $|2(-3) + 1| = |-5| = 5 > 3$ ✓. Try $x = 2$: $|2(2) + 1| = |5| = 5 > 3$ ✓. Try $x = 0$: $|2(0) + 1| = |1| = 1 < 3$ ✗