$sqrt{3x - 22}=sqrt{-x + 10}$

Explanation:

Step1: Square both sides

Since $\sqrt{a}=\sqrt{b}$ implies $a = b$, we have $3x - 22=-x + 10$.

Step2: Add $x$ to both sides

$3x+x-22=-x+x + 10$, which simplifies to $4x-22 = 10$.

Step3: Add 22 to both sides

$4x-22 + 22=10 + 22$, getting $4x=32$.

Step4: Divide both sides by 4

$\frac{4x}{4}=\frac{32}{4}$, so $x = 8$.

Answer:

$x = 8$