SAT Math · Algebra

Linear Inequalities on the Digital SATWhat it tests, how to approach it, and where students get trapped

Solving and interpreting inequalities in one or two variables, including flipping the inequality sign and identifying solution regions.

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Linear Inequalities in Our Question Bank

Total questions

Easy

Medium

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Algebra.

What the SAT Actually Tests

Inequality questions test the same solving skills as equations plus two extra ideas: the inequality sign flips when you multiply or divide by a negative, and solutions are regions rather than points. Two-variable versions ask which point satisfies an inequality (or a system of them), or how a shaded graph region corresponds to the algebra.

For one-variable questions, solve like an equation and watch the sign at every negative multiply/divide. For two-variable questions, the fastest reliable move is testing points — plug the candidate point into the inequality and check. For word problems ("at least," "no more than"), translate the phrase to the symbol before doing anything else.

Original Linear Inequalities Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy

Which ordered pair (x, y) satisfies the inequality 7x − 4y < 10?

A)(4, 3)B)(2, 1)C)(3, 6)D)(5, 5)

Question 2medium

A van can carry a maximum weight of 3,200 pounds. During one trip, the van will transport a 450-pound generator as well as several crates. Some crates weigh 60 pounds each and the others weigh 80 pounds each. Which inequality represents the possible combinations of the number of 60-pound crates, x, and the number of 80-pound crates, y, the van can transport during one trip if only the generator and crates are being hauled?

A)60x + 80y ≤ 2,750B)60x + 80y ≥ 2,750C)60x + 80y ≤ 3,200D)60x + 80y ≥ 3,200

Traps to Avoid

Forgetting to flip the inequality when dividing by a negative — the classic.
Translating "at least 50" as x > 50 instead of x ≥ 50; the boundary matters and answer choices exploit it.
On systems of inequalities, finding a point that satisfies one inequality but not checking the other.

Want more official questions for this skill?

The College Board Student Question Bank can filter official SAT questions by section, domain, skill, and difficulty. Read our question-bank workflow guide before choosing a set.

More Algebra Skills

Linear Equations in One Variable

Solving equations of the form ax + b = c, including equations with variables on both sides, fractions, and no-solution or infinite-solution cases.

Linear Equations in Two Variables

Working with equations like y = mx + b: interpreting slope and intercepts, converting between forms, and connecting equations to their graphs.

Linear Functions

Modeling real situations with linear functions — constant rates of change, initial values, and evaluating or interpreting f(x) in context.

Systems of Linear Equations

Solving pairs of linear equations by substitution or elimination, and reasoning about when systems have one, none, or infinitely many solutions.

Continue With Algebra Practice

Practice is sorted by domain and difficulty. On the Free plan you get the first 5 questions of each difficulty in Algebra. Pro opens every question in the bank.

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Last reviewed August 29, 2026 · Grind1600 Editorial Team