Flashcard 13 - Math Flashcard Set for the ACT

Inequalities are solved like equalities, undoing operations performed on a variable to isolate it; however, any time an inequality is multiplied or divided by a negative number, the direction of the inequality sign changes.
When graphing less than and greater than, use a dotted line and shade below or above, respectively.
When graphing less than or equal to and greater than or equal to, use a solid line and shade below or above the line, respectively.

For inequalities involving absolute values: \(\vert 2x + 3 \vert ≤ 4\), rewrite as \(-4 ≤ 2x + 3 ≤ 4\).
For \(-5 ≥ \vert x+6 \vert\), rewrite as \(-5 ≥ x + 6 ≥ 5\).