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SAT Math: Linear Inequalities and Absolute Value (Drill 3)

Drill 3 · Math · Linear Inequalities and Absolute Value

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About This Drill

SAT Math: Linear Inequalities and Absolute Value (Drill 3) is a Math practice drill covering Linear Inequalities and Absolute Value. It contains 5 original questions developed by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT inequality and absolute value questions cover solving and graphing inequalities, identifying feasible regions for systems, and solving absolute value equations and inequalities. This drill includes problems with compound inequalities and contextual applications.

Questions & Explanations

Question 1. What is the solution set for |2x − 5| ≤ 3?

  • A) 1 ≤ x ≤ 4 ✓
  • B) x ≤ 1 or x ≥ 4
  • C) −4 ≤ x ≤ 1
  • D) x ≤ −1 or x ≥ 4

Explanation: |2x − 5| ≤ 3 means −3 ≤ 2x − 5 ≤ 3. Add 5: 2 ≤ 2x ≤ 8. Divide by 2: 1 ≤ x ≤ 4.

Question 2. Which inequality represents 'a number is more than 7 units from 10'?

  • A) |x − 10| < 7
  • B) |x − 10| > 7 ✓
  • C) |x − 7| > 10
  • D) |x + 10| > 7

Explanation: 'More than 7 units from 10' means the distance between x and 10 exceeds 7: |x − 10| > 7.

Question 3. If −3x + 4 > 13, what is the solution?

  • A) x > 3
  • B) x < −3 ✓
  • C) x > −3
  • D) x < 3

Explanation: −3x > 9. Divide by −3 and flip the inequality: x < −3.

Question 4. A factory must produce between 200 and 350 units daily. If the factory produces x units in the first shift and 120 in the second shift, which inequality represents valid first-shift production?

  • A) 80 ≤ x ≤ 230 ✓
  • B) 80 < x < 230
  • C) 200 ≤ x ≤ 350
  • D) x ≥ 200

Explanation: Total = x + 120. Need 200 ≤ x + 120 ≤ 350. Subtract 120: 80 ≤ x ≤ 230.

Question 5. How many solutions does |x + 3| = −2 have?

  • A) Zero ✓
  • B) One
  • C) Two
  • D) Infinitely many

Explanation: Absolute value is always ≥ 0 and can never equal a negative number. No solutions.