Absolute value equations and inequalities

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are negative on this interval. $$|5-x|-|x+3|=|x+1|$$

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval. $$|2x+4|+|-x+1|=2x$$

Find the sum of the zero points of all the absolute-value expressions of the equation. $$|x-3|=|x+9|-|-2+x|$$ (The zero point is the value of $x$ for which the absolute-value expression equals zero.)

Find the inequality which describes the set graphed in the picture.