Evaluate the integral by interpreting it in terms of areas as 0 goes to 12 |2x - 7|dx?

Question

This is my work so far:

2x-7=0
x=7/2

slope = 2; y-int = (0, -7)

Area of a triangle is 1/2BH.

Answer 1

I can't make sense of what you did. If you want areas, you have to do it in two integrals (triangles)
x goes from 0 to 3.5
INT (7-2x) dx
Area=1/2 b H=1/2 3.5 *7
and x goes from 3.5 to 12
int (2x-7)dx
area=1/2 b H= 1/2 (12-3.5)(24-7)

Answer 2

I added the two areas up and got 84.5 which is the correct. Thanks!

Answer 3

One quick question, for the "area=1/2 b H= 1/2 (12-3.5)(24-7)", how did you get the 24?