SAT Linear Inequalities Worksheet

What this worksheet covers

Linear Inequalities belongs to the Algebra domain on the Digital SAT Math section.

Use this as a one-skill worksheet before timed modules. The goal is not just to get questions right, but to recognize the pattern quickly under SAT timing.

• Official skill: Linear inequalities in one or two variables
• Section: Math
• Domain: Algebra
• Best use: focused drill session before a timed module

Rules to remember

Before drilling this skill, memorize the core rules below and keep them next to your scratch work.

• 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 (<, >).

Practice routine

Start untimed until you can explain the pattern. Then switch to timed sets so the skill holds up inside a full module.

• Do 10 warmup questions and write down every mistake type.
• Do 20 timed questions from the same skill.
• Review missed questions without looking at the explanation first.
• Repeat the misses 48 hours later to confirm the fix stuck.

How to use this on real SAT questions

Linear Inequalities questions are easiest to improve when you practice the recognition step before the calculation step. First identify the Algebra pattern, then choose the fastest method.

Inside the bank, start untimed until you can explain why the answer works. Then rerun the same skill under time pressure and review only the misses and guesses.

• 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 this question type

Linear Inequalities questions usually signal themselves through the representation they give you: an equation, table, graph, short passage, or answer-choice pattern tied to Algebra. Do not start calculating until you have named the pattern.

On a real module, the fastest students first decide whether the question is asking for a value, a relationship, an interpretation, or a rewritten form. That decision tells you which tool to use.

• Look for wording connected to Linear inequalities in one or two variables.
• Identify whether the answer should be a number, expression, sentence, or interpretation.
• Underline the exact value or claim the question asks for before touching the answer choices.
• Flip the inequality sign when you multiply or divide by a negative number.
• Graphing a system of inequalities = overlap of shaded half-planes.

90-minute drill block

Use this sequence when the page is no longer just reading material. The goal is to convert the topic into score movement.