Discussion

Explanation:

A = |x + 3| + |x - 2| - |2x - 8|

The critical points are -3, 2 and 4.

Case 1: x ≥ 4
∴ A = x + 3 + x - 2 - (2x - 8) 
⇒ A = 2x + 1 - 2x + 8
⇒ A = 9

Case 2: 2 ≤ x < 4
∴ A = x + 3 + x - 2 + (2x - 8) 
⇒ A = 2x + 1 + 2x - 8
⇒ A = 4x - 7
∴ A ∈ [1, 9)

Case 3: -3 ≤ x < 2
∴ A = x + 3 - (x - 2) + (2x - 8) 
⇒ A = x + 3 - x + 2 + 2x - 8
⇒ A = 2x - 3
∴ A ∈ [-9, 1)

Case 4: x < -3
∴ A = - (x + 3) - (x - 2) + (2x - 8) 
⇒ A = - x - 3 - x + 2 + 2x - 8
⇒ A = - 9

From the above cases, The maximum value of |A| = 9

Hence, option (b).

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