Answer: x = -4
Work Shown
f(x) = -2
3x+10 = -2
3x = -2-10
3x = -12
x = -12/3
x = -4
The input x = -4 leads to the output f(x) = -2. One way to check, would be to have this scratch work.
f(x) = 3x+10
f(-4) = 3(-4)+10
f(-4) = -12+10
f(-4) = -2
This confirms the answer.
Another way to confirm the answer is to use GeoGebra or Desmos to graph y = 3x+10 and y = -2. The two lines intersect at (-4,-2) to indicate f(-4) = -2. Therefore, x = -4.