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

Just like parentheses in arithmetic, you must work from the inside out! Start with $|-4 + 8| = 4$, then $|-2| = 2$, before tackling the final inequality.

If you get something like $|expression| < 0$, there's no solution because absolute values are never negative. But $|expression| > 0$ means the expression inside cannot equal zero.

This means a is between -2 and 2, but doesn't include the endpoints. So $a = 1.5$ works, but $a = 2$ or $a = -2$ don't work.

Absolutely! Try $a = 1$: the original expression becomes $|4-2|-|1| = 2-1 = 1 > 0$ ✓. Try $a = 3$: you get $2-3 = -1 < 0$, so it's outside our solution!

When $a = 2$, we get $|2-2| = |0| = 0$, but we need the result to be greater than 0. The inequality is strict, so we exclude the boundary values.