SAT and ACT math terms · SAT Math, ACT Math
Linear inequality
Linear inequality: A statement that compares two linear expressions using <, >, ≤ or ≥, with a range of solutions.
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What it means
Linear inequalities are solved like equations, with one key rule: multiplying or dividing both sides by a negative number reverses the inequality sign. Solutions in two variables are shaded regions on a graph.
Word problems often use phrases such as at most (≤) and at least (≥).
Example
−3x + 7 ≤ 22 → −3x ≤ 15 → x ≥ −5. Dividing by −3 flips ≤ to ≥.
On the exam
Expect inequalities in word problems about budgets and limits, and questions about which point lies in a solution region.