Segment addition and subtraction Algebra

Question

Point B is on line segment \overline{AC}AC. Given AB=2x+10,AB=2x+10, BC=x,BC=x, and AC=5x,AC=5x, determine the numerical length of \overline{AC}.AC.



Answer 1

By segment addition postulate

AB + BC = AC

substituting the expressions given:

2x + 10 + x = 5x

10 = 2x

x = 5

since AC = 5x = 5 * 5 = 25