SAT Linear Inequalities

Linear inequalities work like linear equations with two additions: the direction of the sign flips when you multiply or divide by a negative, and the answer usually has to be read back into the situation — a capacity, a minimum, a feasible range.

Practise this skill freeHow the SAT is structured
MathAlgebra76 questions
The trap on this skill

Using the total capacity without subtracting the container weight first.

How this skill behaves

What 76 questions on it look like

89% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

Not one question in this skill is rated hard. What makes it cost marks is speed and carelessness, not difficulty.

medium89%
easy11%

Difficulty mix across the 76 questions in this skill.

From the bank

Three real linear inequalities questions

Each one explains the credited answer and why every other option fails.

Algebra · medium

The workroom wide cart filing price tag has a budget of at most 62 dollars for kits related to headline specificity only for examples that met the stated rule for the upper-shelf examples. A case costs 7 dollars, and each added kit costs 5 dollars. What is the greatest number of kits that can be added?

  1. A12
  2. B10
  3. C11correct
  4. D13
Why C is correct — and why the others are not

The inequality is 7 + 5p <= 62. Subtract 7 to get 5p <= 55, so p <= 11. The greatest whole number of packets is 11. That reasoning is tied to the item-specific detail about Linear inequalities. A final check is keeping the variable definition fixed through the solution.

A. This value results from using the total capacity without subtracting the container weight first

B. This value results from using the total capacity without subtracting the container weight first

D. This value results from using the total capacity without subtracting the container weight first

Algebra · easy

The rooftop weekend mural plotting layout note has a budget of at most 23 dollars for kits related to sensor density after the team checked a second measure for the green-version examples. A case costs 5 dollars, and each added kit costs 2 dollars. What is the greatest number of kits that can be added?

  1. A10
  2. B8
  3. C9correct
  4. D11
Why C is correct — and why the others are not

The inequality is 5 + 2p <= 23. Subtract 5 to get 2p <= 18, so p <= 9. The greatest whole number of packets is 9. This is the only choice that stays consistent with the detail about Linear inequalities. A final check is simplifying only after the equivalent structure is preserved.

A. This value results from using the total capacity without subtracting the container weight first

B. This value results from using the total capacity without subtracting the container weight first

D. This value results from using the total capacity without subtracting the container weight first

Algebra · medium

A shipment for the stadium narrow tile tracking fit guide can weigh at most 32 kilograms. Packing material weighs 8 kilograms, and each instrument for tracking button placement when the same definition was used throughout for the second-room cases weighs 2 kilograms. What is the greatest number of instruments in the shipment?

  1. A13
  2. B11
  3. C16
  4. D12correct
Why D is correct — and why the others are not

The inequality is 8 + 2p <= 32. Subtract 8 to get 2p <= 24, so p <= 12. The greatest whole number of packets is 12. This matches the evidence or condition involving Linear inequalities. A final check is matching the final number to the quantity described in words.

A. This value results from using the total capacity without subtracting the container weight first

B. This value results from using the total capacity without subtracting the container weight first

C. This value results from using the total capacity without subtracting the container weight first

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FAQ

Linear Inequalities questions

When does the inequality sign flip?

Only when you multiply or divide both sides by a negative number. Adding or subtracting never flips it.

How do I answer "greatest number of" questions?

Solve the inequality, then take the largest whole value that satisfies it — and check whether the problem already subtracted something, like the weight of a container.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Systems of Linear Equations135 questionsLinear Equations in One Variable128 questionsLinear Equations in Two Variables127 questionsLinear Modeling / Word Problems124 questions

Practise linear inequalities until the trap stops working.

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