Linear inequalities

About this lesson

Linear inequalities on the SAT: solving and flipping the sign when multiplying or dividing by a negative, compound inequalities and counting integer solutions, translating at least / at most, building systems of inequalities from word problems, and testing points in the solution region.

On the Digital SAT, linear inequalities are their own skill in the Algebra domain. They come in three main shapes: solving a single or compound inequality, a word problem asking for the greatest or least quantity that fits a budget or capacity, and a system of two inequalities where you pick the point that works or the system that matches the situation.

Points are usually lost on small details rather than arithmetic: not flipping the sign after dividing by a negative, rounding 23.4 up to 24 in a "greatest number" question, missing one endpoint when counting integers, or checking only one inequality of a system. This lesson targets exactly those spots, with a phrase-to-symbol table and Desmos tricks for shading regions and testing points. It ends with 6 self-graded practice questions, each with a full explanation.