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Find the solution set of |3 - 2x| ≤ 5.

Correct answer: C. 1 ≤ x ≤ 4

  • A. x ≤ 4
  • B. -4 ≤ x ≤ -1
  • C. 1 ≤ x ≤ 4
  • D. x ≥ 4

Explanation

The correct answer is c) 1 ≤ x ≤ 4.To find the solution set, we need to solve the inequality |3 - 2x| ≤ 5.Solving the inequality:|3 - 2x| ≤ 5-5 ≤ 3 - 2x ≤ 5-8 ≤ -2x ≤ 24 ≥ x ≥ 1Therefore, the solution set is 1 ≤ x ≤ 4.Explanation:The given inequality |3 - 2x| ≤ 5 can be interpreted as the set of values of x for which the absolute value of (3 - 2x) is less than or equal to 5.This means that the values of x must satisfy the following two conditions:3 - 2x ≤ 5-(3 - 2x) ≤ 5Solving these conditions, we get:3 - 2x ≤ 5-2x ≤ 2x ≥ 1-(3 - 2x) ≤ 52x - 3 ≥ -52x ≥ -2x ≤ 4Therefore, the solution set is the intersection of these two conditions, which is 1 ≤ x ≤ 4.

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