Answer
$x = 3$
Work Step by Step
These two angles are same-side exterior angles, meaning they lie on the same side of the transversal but outside of the parallel lines. Same-side exterior angles are supplementary, so we can add the two angles together and set them equal to $180^{\circ}$.
$(\frac{3x - 4}{2}) + (4x + \frac{x}{2} + 2) = 180$
$\frac{3x - 4}{2} + \frac{8x}{2} + \frac{x}{2} + 2 = 180$
$\frac{3x - 4 + 8x + x}{2} + 2 = 180$
Combine like terms:
$\frac{12x - 4}{2} + 2 = 180$
Simplify the fraction by dividing both the numerator and denominator by their greatest common denominator, $2$:
$6x - 2 + 2 = 180$
Combine like terms:
$6x = 180$
Divide both sides by $6$ to solve for $x$:
$x = 30$
