Question

Points A, B, and C are collinear. Point B is between A and C. Solve for x if AB = x + 17, AC = 20, and BC = x + 13.

Answer 1

x is -5.

Explanation:

*------------*------*

A B C

If point B is between A and C, then AB+BC=AC by segment addition postulate.

So we have the following equation to solve:

(x+17)+(x+13)=20

Distribute:

x+17+x+13=20

Reorder using commutative property:

2x+30=20

Subtract 30 on both sides (subtraction property):

2x=-10

Divide both sides by 2 (division property):

x=-5

So if x=-5, then

AB=x+17=-5+17=12

BC=x+13=-5+13=8

and AC=12+8=20.