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      Question

      Solve for x: |2x βˆ’ 5| + |x + 1| ≀

      10.
      A x ∈ [5, 14/3]. Correct Answer Incorrect Answer
      B x ∈ [βˆ’2, 11/3]. Correct Answer Incorrect Answer
      C x ∈ [βˆ’2, 14/3]. Correct Answer Incorrect Answer
      D x ∈ [βˆ’9, 4/3]. Correct Answer Incorrect Answer

      Solution

      ATQ,

      Critical points at x = 2.5 and x = βˆ’1. Case 1: x β‰₯ 2.5 β‡’ (2x βˆ’ 5) + (x + 1) ≀ 10 β‡’ 3x βˆ’ 4 ≀ 10 β‡’ x ≀ 14/3. So 2.5 ≀ x ≀ 14/3. Case 2: βˆ’1 ≀ x ≀ 2.5 β‡’ (5 βˆ’ 2x) + (x + 1) ≀ 10 β‡’ 6 βˆ’ x ≀ 10 β‡’ βˆ’x ≀ 4 β‡’ x β‰₯ βˆ’4. In this band, it’s all valid: βˆ’1 ≀ x ≀ 2.5. Case 3: x ≀ βˆ’1 β‡’ (5 βˆ’ 2x) + (βˆ’x βˆ’ 1) ≀ 10 β‡’ 4 βˆ’ 3x ≀ 10 β‡’ βˆ’3x ≀ 6 β‡’ x β‰₯ βˆ’2. So in this band: βˆ’2 ≀ x ≀ βˆ’1. Combine: βˆ’2 ≀ x ≀ 14/3. Answer: x ∈ [βˆ’2, 14/3].

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