Linear Inequalities: SAT Practice Questions

78 official Linear Inequalities questions (Algebra) from the SAT Suite Question Bank. Pick any question from the list, or start with Question 1. Every question shows the answer and a full explanation, with step-by-step Desmos solutions available for most questions. It is free, and no account is needed.

Start with Question 1

What does Linear Inequalities test on the SAT?

Linear Inequalities questions ask for a range of valid values or a shaded region satisfying one or more conditions. Inequality direction and boundary inclusion matter as much as the arithmetic.

Common question types

Solve a one-variable inequality
Model a minimum or maximum constraint
Identify the graph or region satisfying inequalities

Common traps

Forgetting to reverse the sign after multiplying or dividing by a negative
Using a strict boundary when equality is allowed
Testing a point on the boundary instead of inside a region

Difficulty distribution

Start with the easier questions, then work toward the highest score bands.

Easy: 29
Medium: 29
Hard: 20
Extreme: 0

Start here

FoundationQuestion 12Easy SAT question IntermediateQuestion 51Medium SAT question ChallengeQuestion 78Hard SAT question

How do I improve at Linear Inequalities?

1Translate words such as at least and fewer than before solving.
2Mark whether each boundary is included.
3Test a simple point in the proposed interval or shaded region.

Desmos method

Enter the inequality directly to view its solution region. For systems, graph every inequality together and identify the overlap, checking whether boundary lines are solid or dashed.

All 78 official questions

In the same order as the list on the left. Each one opens in practice mode.