➕ Algebra 1 · Inequalities
Compound 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.
And versus or
- AND: both true, so keep the overlap (narrower)
- OR: at least one true, so keep everything shaded (wider)
- In math, “or” allows both to be true
Forms
- a < x ≤ b means x > a and x ≤ b
- “Or” stays as two pieces: x < a or x ≥ b
- Interval notation: (a, b] for “and”, ∪ for “or”
Solving
- Three parts: same move on all three parts
- Multiply or divide by a negative: reverse both signs, then put the smaller number first
- Two pieces: solve each, graph each, combine
Special results
- “And” with no overlap: no solution
- “Or” covering the whole line: every real number
- x ≥ c and x ≤ c: only x = c
- x < c or x > c: every real number except c
Words
- at least: ≥. at most: ≤. more than: >. fewer than: <
- between or from … to …: usually “and”. Check whether the ends count.
- Define the variable in words. Give units.
Formulas
- Three-part “and” form: a < x ≤ b means x > a and x ≤ b
- Interval notation: −2 < x ≤ 5 is (−2, 5]. “Or” uses ∪: x < −6 or x ≥ 7 is (−∞, −6) ∪ [7, ∞).
- Edge cases: x ≥ c and x ≤ c: only x = c. x < c or x > c: every real number except c.
Compound Inequalities cheat sheet from HighSchoolQ.com, for personal study use.