Final answer:
By equating the expressions for alternate interior angles <3 and <4, we solve the equation and find that x equals 7.
Step-by-step explanation:
If <3 and <4 are alternate interior angles, this entails that they are equal. Thus, by setting the equations 15x-7 for <3 and 12x+14 for <4 equal to each other, we can solve for x. We get:
15x - 7 = 12x + 14
Subtracting 12x from both sides, we have:
3x - 7 = 14
Then, adding 7 to both sides gives us:
3x = 21
Dividing both sides by 3, we get:
x = 7