Exponential Inequality

Algebra Level 3

Let \(a\) and \(b\) be the minimum and maximum values of \(x\), respectively, that satisfy the inequality \[ 2 ^x (2 \cdot 2 ^x + 8) \leq 8 ^x (5 - 2 ^x). \] What is the value of \( a + b? \)

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