➕ Algebra 1 · Inequalities
Solving Inequalities cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
Symbols and circles
- < and >: open circle (boundary not included)
- ≤ and ≥: closed circle (boundary included)
- Say it with x first, then shade: x > 3 shades right, x < 3 shades left
Sign rules (FLIP)
- Add or subtract: the sign stays
- Multiply or divide by a positive number: the sign stays
- Multiply or divide by a negative number: reverse the sign
Words
- at least: ≥. at most: ≤
- more than: >. fewer than: <
- Define the variable first. Interpret the answer.
Special results
- Variable vanishes, leftover true (1 > 0): every real number
- Variable vanishes, leftover false (1 < 0): no solution
Example
- 5 − 4x ≥ 17
- −4x ≥ 12 (subtract 5)
- x ≤ −3 (divide by −4, reverse the sign)
Formulas
- Add, or multiply by a positive: sign stays: If a < b, then a + c < b + c for any number c. If also c > 0, then ac < bc.
- Negative multiplier: sign reverses: If a < b and c < 0, then ac > bc and a/c > b/c
- Words to symbols: at least: ≥. at most: ≤. more than: >. fewer than: <
Solving Inequalities cheat sheet from HighSchoolQ.com, for personal study use.