Answer x = 22
Step by step
Vertical angles are congruent, so they are equal to each other. We can equal both of these vertical angles and solve.
3x -14 = 4 (x - 9)
Distribute
3x -14 = 4x - 36
Subtract 4x from both sides to isolate variable
3x -4x -14 = 4x -4x -36
Simplify
-x -14 = -36
Add 14 to both sides to solve for x
-x -14 + 14 = -36 +14
Simplify
-x = -22
Multiply both sides by -1 to change the signs
x = 22