(5 - 2)2 - 2(x + 4) > 23 - 38 + 82

To solve the inequality \((5 - 2)2 - 2(x + 4) > 23 - 38 + 82\), let's simplify both sides step by step.

1. Start with the left side: \[ (5 - 2)2 = 3 \cdot 2 = 6 \] So, the left side becomes: \[ 6 - 2(x + 4) \]

   Now distribute \(-2\) to \(x + 4\): \[ = 6 - 2x - 8 \] This simplifies to: \[ = -2x - 2 \]

2. Now let's simplify the right side: \[ 23 - 38 + 82 \] First, calculate \(23 - 38\): \[ = -15 \] Then add \(82\): \[ -15 + 82 = 67 \]

Now we have the simplified inequality: \[ -2x - 2 > 67 \]

3. Next, isolate \(x\): \[ -2x > 67 + 2 \] \[ -2x > 69 \] Now divide both sides by \(-2\) (remember, when you divide by a negative number, you must reverse the inequality): \[ x < \frac{69}{-2} \] This simplifies to: \[ x < -34.5 \]

So the solution to the inequality is: \[ x < -34.5 \]