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SAT Math: Linear Inequalities and Absolute Value (Drill 2)

Drill 2 · Math · Linear Inequalities and Absolute Value

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About This Drill

SAT Math: Linear Inequalities and Absolute Value (Drill 2) is a Math practice drill covering Linear Inequalities and Absolute Value. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT linear inequality and absolute value questions test solving inequalities algebraically, checking points in solution regions, and translating word problems into absolute value notation. This drill includes both single-variable inequalities and two-variable inequality systems.

Questions & Explanations

Question 1. y ≤ 2x + 3 and y > −x + 1. Which point is in the solution region?

  • A) (0, 5)
  • B) (2, 3) ✓
  • C) (−3, 0)
  • D) (0, 0)

Explanation: Test (2, 3): 3 ≤ 2(2) + 3 = 7 ✓. 3 > −2 + 1 = −1 ✓. Both satisfied.

Question 2. What is the product of all values of x that satisfy |3x − 6| = 15?

  • A) −21 ✓
  • B) −10
  • C) 21
  • D) 4

Explanation: 3x − 6 = 15 gives x = 7. 3x − 6 = −15 gives x = −3. Product = 7 × (−3) = −21.

Question 3. What is the solution to (4x + 8)/2 ≥ 10?

  • A) x ≥ 2
  • B) x ≥ 2.5
  • C) x ≥ 3 ✓
  • D) x ≥ 6

Explanation: Multiply by 2: 4x + 8 ≥ 20. Subtract 8: 4x ≥ 12. x ≥ 3.

Question 4. Which represents the solution to |x| > 6?

  • A) −6 < x < 6
  • B) x > 6
  • C) x < 6
  • D) x 6 ✓

Explanation: |x| > 6 means distance from 0 is greater than 6: x 6.

Question 5. A student's test score s must be within 10 points of 80 to qualify. Which inequality represents qualifying scores?

  • A) |s − 80| ≤ 10 ✓
  • B) |s − 10| ≤ 80
  • C) |s + 80| ≤ 10
  • D) s − 80 ≤ 10

Explanation: 'Within 10 of 80' means |s − 80| ≤ 10, which expands to 70 ≤ s ≤ 90.