Answer
$$z=-2,\:y=3,\:x=1$$
Work Step by Step
To solve, we first must isolate one of the variables to solve for that variable. Then, we use that value to solve for the other two variables:
$$\frac{10-\left(-\frac{-5z-22}{4}\right)+2z}{3}+4\left(-\frac{-5z-22}{4}\right)+3z=7 \\ z=-2$$
Thus:
$$y=-\frac{-5\left(-2\right)-22}{4}=3$$
$$x=\frac{10-3+2\left(-2\right)}{3}=1$$
