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SAT Math / Algebra

SAT topic

Inequalities

Solution sets that stay true across a range of values.

Learning goals

  • Solve a linear inequality and describe the solution as a set or interval.
  • Reverse the inequality sign when multiplying or dividing by a negative number.

Explanation

An inequality says one quantity is larger or smaller than another, not that the two sides are equal. You can add or subtract on both sides the same way you would with an equation. The special rule is that multiplying or dividing by a negative number flips the inequality sign.

On the SAT, inequalities often appear as a line on a number line, as a shaded half-plane, or as a word problem with a minimum or maximum. Translate 'at least' to ≥ and 'no more than' to ≤ before you solve. Then test one number from your solution set in the original sentence.

Common mistakes

  • Forgetting to flip the sign after dividing by a negative.
  • Treating a strict inequality as if the endpoint were included.

Practice

1 of 2Percent problems · easy · multiple choice

A quantity increases from 50 to 65. What is the percent increase?

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Quick review

  1. 01Isolate the variable using the same steps as an equation.
  2. 02Flip the sign if you multiply or divide by a negative.
  3. 03Test one interior point in the original inequality.
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Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

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    Official SAT practice hub

    College Board SAT practice landing page, including links to tests and tools.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

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    Bluebook full-length practice

    Official digital SAT practice tests in the Bluebook app.

    College Board · All rights reserved · accessed 2026-10-01

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    Student Question Bank

    Official SAT practice questions hosted by College Board.

    College Board · All rights reserved · accessed 2026-10-01

    Use as an external link. Do not republish question stems.

    Open source

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    Official SAT Prep on Khan Academy

    College Board describes this as free Official SAT Prep with lessons, hints, and walkthroughs.

    Khan Academy / College Board · All rights reserved · accessed 2026-10-01

    Open source

  • Reference only — do not copy

    OpenStax College Algebra 2e

    Algebra reference; current terms include noncommercial and AI-ingestion limits.

    OpenStax · Restricted — see publisher page · accessed 2026-10-01

    Open source