Math · Algebra

Linear Inequalities

Solve and interpret one- and two-variable linear inequalities.

What the SAT Tests

Linear inequality questions test the same algebra muscles as equations, but require careful attention to inequality flips when multiplying or dividing by negatives.

Key Tips for Linear Inequalities

Flip the inequality sign when you multiply or divide by a negative number.
Graphing a system of inequalities = overlap of shaded half-planes.
Always re-read to see whether the boundary line is included (≤, ≥) or excluded (<, >).

How to recognize Linear Inequalities questions

Look for Algebra signals: equations, graphs, tables, variables, units, or words that describe a relationship.
Before solving, decide whether the answer should be a value, expression, coordinate, graph feature, or interpretation.
The official College Board skill label is Linear inequalities in one or two variables; match your practice misses to that label when reviewing.

Fast solving workflow

Translate the givens into an equation, graph, table, or labeled diagram before using answer choices.
Choose the fastest method: mental math for one-step work, paper algebra for clean symbolic steps, Desmos for intersections/tables/roots, and substitution for ordered answer choices.
Check the final answer against the question stem, especially units, signs, and whether it asks for x, y, a sum, a coefficient, or an interpretation.

Common traps

Solving for the wrong variable after doing the algebra correctly.
Dropping a negative sign when moving terms across the equals sign.
Reading slope or intercept without checking the units in the problem.

Sample Linear Inequalities Questions

These are real practice questions pulled from our Digital SAT bank. Try each one before reading the highlighted correct answer.

Question 1 · Easy
$y = 84 (x - 3) + 287$
Which equation is equivalent to the given equation?
- A. $y = 84 x + 287$
- B. $y = 287 x + 539$
- C. $y = 84 x + 35$ Correct
- D. $y = 287 x + 84$
Question 2 · Easy
A dog has a mass of 42 kilograms. What is the dog's mass, in grams? (1 kilogram = 1,000 grams)
- A. 42,000Correct
- B. 1,764
- C. 1,042
- D. 958
Question 3 · Easy
$0.72 x - 3 \leq 15$ represents the number of pears, $x$ , that the shopper can purchase for no more than $15.
- A. $0.72 x + 3 \leq 15$
- B. $0.72 + 3 \geq 15$
- C. $0.72 x - 3 \leq 15$ Correct
- D. $0.72 x - 3 \geq 15$

Practice Linear Inequalities Questions

Drill linear inequalities questions in the Digital SAT Math question bank, or take a full-length practice module to see how this skill appears under test conditions.

Practice block	What to do	Move on when
Warmup	Solve 10 untimed linear inequalities questions and write the rule used for each.	You can explain 8 of 10 without reading the explanation.
Timed drill	Solve 20 filtered bank questions at real module pace.	Accuracy is at least 80% and misses are not repeating.
Transfer	Take a mixed timed module and mark each Algebra miss.	The skill still holds up when mixed with other question types.

FAQs

What is Linear Inequalities on the Digital SAT?

Linear inequality questions test the same algebra muscles as equations, but require careful attention to inequality flips when multiplying or dividing by negatives.

How hard are linear inequalities questions?

Linear Inequalities questions appear at every difficulty level on the Digital SAT Math section. The hardest versions gate access to the top scaled scores in the hard Module 2.

How do I practice linear inequalities?

Use the 1600.now question bank to filter for linear inequalities questions, solve at least 20 in a row, and review every miss with the written explanation.

Related Math Skills

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