Solve the Inequality: |−4 + 8| − 2|−|a| > 0

Let's solve the inequality step-by-step:

First, simplify $|-2|$.

• $|-2| = 2$, because the absolute value of a number is its distance from zero without considering the sign.

Now focus on the expression $|-4 + 8|$.

• $-4 + 8 = 4$, so $|-4 + 8| = |4| = 4$.

Substitute these values back into the inequality:

• The inequality becomes $|4 - 2| - |a| > 0$.

Simplify further:

• $4 - 2 = 2$, so $|2 - |a|| > 0$.

Now we solve $|2 - |a|| > 0$:

• This inequality implies that $2 - |a| \neq 0$, meaning $|a| \neq 2$.
• Additionally, $|2 - |a|| > 0$ implies $2 - |a| > 0 \text{ or } -1(2 - |a|) > 0$, simplifying to $|a| < 2$.

Since $|a| < 2$ implies that $-2 < a < 2$, solve for $a$:

$-2 < a < 2$

Thus, the solution set is:

$2 > a > -2$