Question

M is the midpoint of AB , AM=3x+3, and AB=8x−6. What is the length of MB ?

Answer 1

|AM| = |MB|

|AB| = |AM| + |MB| ⇒ |AB| = 2|AM|

|AB| = 8x - 6; |AM| = 3x + 3

subtitute:

8x - 6 = 2(3x + 3) |use distributive property: a(b + c) = ab + ac

8x - 6 = 6x + 6 |add 6 to both sides

8x = 6x + 12 |subtract 6x from both sides

2x = 12 |divide both sides by 2

x = 6

|MB| = 3x + 3, subtitute

|MB| = 3 · 6 + 3 = 18 + 3 = 21