Solve and graph linear and compound inequalities with interval notation and number line visualization.
Solve like an equation — with one key exception
Addition / Subtraction: Add or subtract the same value from both sides — the inequality direction stays the same.
Multiply / Divide by a positive: The inequality direction stays the same.
Multiply / Divide by a negative: The inequality sign FLIPS.
3x < 9 → x < 3 (divide by +3, no flip)
−3x < 9 → x > −3 (divide by −3, FLIP!)
( ) = open (strict) | [ ] = closed (includes)
| Inequality | Interval Notation |
|---|---|
| x < a | (-∞, a) |
| x ≤ a | (-∞, a] |
| x > a | (a, ∞) |
| x ≥ a | [a, ∞) |
| a < x < b | (a, b) |
| a ≤ x ≤ b | [a, b] |
| x < a OR x > b | (-∞, a) ∪ (b, ∞) |
One-on-one Algebra tutoring builds the intuition for when to flip the sign and how to read interval notation — we work through your actual homework so it sticks.