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SAT Math: Linear Inequalities and Absolute Value (Drill 1)

Drill 1 · Math · Linear Inequalities and Absolute Value

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About This Drill

SAT Math: Linear Inequalities and Absolute Value (Drill 1) 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 questions ask you to solve inequalities, interpret their solutions on a number line, and identify solution regions for systems of inequalities. Absolute value questions involve equations and inequalities of the form |ax + b| ≥ c, requiring two-case analysis.

Questions & Explanations

Question 1. Which of the following represents all values of x that satisfy the inequality 3x − 7 > 8?

  • A) x > 3
  • B) x < 5
  • C) x > 5 ✓
  • D) x > 15

Explanation: Add 7 to both sides: 3x > 15. Divide by 3: x > 5.

Question 2. What is the solution to the inequality −2x + 6 ≤ 12?

  • A) x ≤ −3
  • B) x ≤ 3
  • C) x ≥ 3
  • D) x ≥ −3 ✓

Explanation: Subtract 6 from both sides: −2x ≤ 6. Divide by −2 and reverse the inequality sign: x ≥ −3. The sign reversal when dividing by a negative number is the key step many students miss.

Question 3. What is the sum of all values of x that satisfy |x − 4| = 7?

  • A) 8 ✓
  • B) 14
  • C) 4
  • D) 7

Explanation: Split into two equations: x − 4 = 7 gives x = 11, and x − 4 = −7 gives x = −3. The sum is 11 + (−3) = 8. For any equation |x − a| = b, the sum of the two solutions always equals 2a.

Question 4. A catering company charges a $50 setup fee plus $12 per guest. If a client has a budget of no more than $200, what is the maximum number of guests the client can invite?

  • A) 11
  • B) 12 ✓
  • C) 13
  • D) 15

Explanation: Set up the inequality: 50 + 12n ≤ 200. Subtract 50: 12n ≤ 150. Divide by 12: n ≤ 12.5. Since the number of guests must be a whole number, the maximum is 12.

Question 5. Which of the following represents the solution to |2x + 1| < 9?

  • A) x < 4
  • B) x > −5 for the inequality shown
  • C) x 4
  • D) −5 < x < 4 ✓

Explanation: For |2x + 1| < 9, write the compound inequality: −9 < 2x + 1 < 9. Subtract 1: −10 < 2x < 8. Divide by 2: −5 < x 9 (the opposite inequality).