21Number 21ExplanationIf b>ab > ab>a, the value of xxx that satisfies ∣x−2a∣+a≤b|x - 2a| + a \leq b∣x−2a∣+a≤b is....3a≤x≤2b+a3a \leq x \leq 2b + a3a≤x≤2b+ax≥−b+3ax \geq -b + 3ax≥−b+3ax≤b+ax \leq b + ax≤b+ab−3a≤x≤−b+ab - 3a \leq x \leq -b + ab−3a≤x≤−b+a−b+3a≤x≤b+a-b + 3a \leq x \leq b + a−b+3a≤x≤b+aExplanationSolve the inequality ∣x−2a∣+a≤b|x - 2a| + a \leq b∣x−2a∣+a≤b∣x−2a∣≤b−a|x - 2a| \leq b - a∣x−2a∣≤b−a−(b−a)≤x−2a≤b−a-(b - a) \leq x - 2a \leq b - a−(b−a)≤x−2a≤b−a−b+a≤x−2a≤b−a-b + a \leq x - 2a \leq b - a−b+a≤x−2a≤b−a Add 2a2a2a to both sides −b+a+2a≤x−2a+2a≤b−a+2a-b + a + 2a \leq x - 2a + 2a \leq b - a + 2a−b+a+2a≤x−2a+2a≤b−a+2a−b+3a≤x≤b+a-b + 3a \leq x \leq b + a−b+3a≤x≤b+a Therefore the solution is −b+3a≤x≤b+a-b + 3a \leq x \leq b + a−b+3a≤x≤b+a.
