MathAlgebraMedium frequency

SAT Math: Setting Up Inequalities from Word Problems

26+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    Identify the constraint: "at least" → ≥, "at most" → ≤, "more than" → >, "fewer than" → <.

  • 2

    Set up the inequality the same way you would a linear equation, but use the correct inequality symbol.

  • 3

    The solution is a range of values — check the boundary case and values inside the range.

  • 4

    For two-variable inequalities, points in the shaded region satisfy the inequality; points on the boundary satisfy it if the line is solid (≤ or ≥).

  • 5

    Always re-read whether the answer should be the inequality itself or a specific value that satisfies it.

Common mistakes
  • Confusing "at least 10" (≥ 10) with "at most 10" (≤ 10) — these are opposite constraints.
  • Solving the algebraic inequality correctly but then answering with the boundary value rather than a value in the valid range.
Try a sample question

SAT-style practice

A car can carry at most 800 pounds. Each box weighs 25 pounds. Which inequality gives the maximum number of boxes n the car can carry?

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