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SAT Math

Linear Inequalities

Linear Inequalities is a skill in the Algebra domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

A bakery packs muffins into boxes. Each box holds at least 12 muffins but no more than 18 muffins. Which of the following could be the total number of muffins in 5 boxes?
  1. A. 95
  2. B. 100
  3. C. 80 ✓
  4. D. 55

Correct answer: C. Since each box holds between 12 and 18 muffins, 5 boxes hold between 5(12) = 60 and 5(18) = 90 muffins; 80 falls within this range.

Which value of x satisfies the inequality 3(x − 4) ≥ 2x − 5?
  1. A. 6
  2. B. 5
  3. C. 4
  4. D. 7 ✓

Correct answer: D. Simplifying gives 3x − 12 ≥ 2x − 5, so x ≥ 7; substituting x = 7 gives 9 ≥ 9, which is true.

A food pantry packs boxes with canned vegetables and canned fruit. Each can of vegetables weighs 0.9 pound, and each can of fruit weighs 0.7 pound. A packed box must weigh no more than 15 pounds. Which inequality represents this constraint, where v is the number of vegetable cans and f is the number of fruit cans in a box?
  1. A. 0.9v + 0.7f ≤ 15 ✓
  2. B. 0.9v + 0.7f ≥ 15
  3. C. 0.9v + 0.7f ≤ 0.9 + 0.7
  4. D. 0.7v + 0.9f ≤ 15

Correct answer: A. The total weight, 0.9v + 0.7f, must be at most 15 pounds, so the constraint is 0.9v + 0.7f ≤ 15.

A vendor sells popcorn for $4 and lemonade for $3. She wants her total revenue to be at least $150 while selling no more than 45 items total, where x is the number of popcorns sold and y is the number of lemonades sold. Which system of inequalities represents these constraints?
  1. A. 4x + 3y ≥ 150 and x + y ≤ 45 ✓
  2. B. 4x + 3y ≤ 150 and x + y ≥ 45
  3. C. 4x + 3y ≥ 150 and x + y ≥ 45
  4. D. 3x + 4y ≥ 150 and x + y ≤ 45

Correct answer: A. Correct — revenue of at least $150 means 4x + 3y ≥ 150, and selling no more than 45 total items means x + y ≤ 45.

What is the solution set for x in the compound inequality −3 < (2x − 1)/4 ≤ 5?
  1. A. −11 < x ≤ 21
  2. B. −5.5 < x ≤ 10.5 ✓
  3. C. −1.75 < x ≤ 6.25
  4. D. −6.5 < x ≤ 9.5

Correct answer: B. Correct — multiplying all three parts by 4 gives −12 < 2x − 1 ≤ 20, then adding 1 gives −11 < 2x ≤ 21, and dividing by 2 gives −5.5 < x ≤ 10.5.