Point B is on line segment A C ‾ AC . Given A B = 3 x , AB=3x, B C = 4 x + 8 , BC=4x+8, and A C = 5 x + 10 , AC=5x+10, determine the numerical length of A C ‾ . AC .

Answer 1

If B is on AC, then AB plus BC will give us AC. We are told the measures of AB, BC, AC in terms of X. So

we can say:

3X + 4X + 8 = 5X + 10 then simplify and get

2X = 2 so X = 1.

Now plug in that 1 to AC = 5X + 10 and get AC = 15!

Answer 2

By segment addition:

3x + 4x + 8 = 5x + 10

7x + 8 = 5x + 10

-2x = 2

x = -1