Getting wrong answer for absolute value inequality and not sure why

Question

The question:

The function p is defined by $-2|x+4|+10$. Solve the equality $p(x) > -4$

Here were my steps to solving this:

1.) Subtract 10 from both sides -> $-2|x+4| > -14$

2.) Divide both sides by -2 -> $|x+4|>7$

3.) $x+4$ should therefore be 7 units or greater from zero on the number line, meaning either greater than 7 or less than -7:

$x+4 > 7$

$x+4 < -7$

4.) Subtract 4 from both sides:

$x > 3$

$x < -11$

Graphing this, I see my signs are the wrong way round but I'm not quite sure where I've gone wrong.

Answer 1

$20$ is greater than $8$, right?

$$20 > 8$$

Now divide both sides by $-2$:

$$-10 > -4$$

Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $\le$ becomes $\ge$ etc:

$$-10 < -4$$

Answer 2

$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).

The rest is all good.