Question

M is between A and B and M is the midpoint of AB. If AM = 3x - 1 and AB = 40, find x and BM.

A. x = 14, BM = 21
B. x = 9, BM = 31
C. x = 11, BM = 19
D. x = 7, BM = 27

Answer 1

The correct answer is option B. The value of x is 7 and BM is 20.

Step-by-step explanation:

The correct answer is option B. To find the value of x, we can use the fact that M is the midpoint of AB. Since AM is equal to 3x - 1 and AB is equal to 40, we can set up the equation:

AM + MB = AB

Substituting the given values, we have:

3x - 1 + BM = 40

Next, we solve for x:

3x - 1 = 40 - BM

3x = 41 - BM

x = (41 - BM) / 3

Since M is the midpoint of AB, BM is equal to AM, which is 3x - 1. So, we can substitute BM = 3x - 1 in the equation:

x = (41 - (3x - 1)) / 3

Simplifying the equation, we get:

3x = 42 - 3x

6x = 42

x = 7

To find BM, we substitute the value of x back into the equation for BM:

BM = 3x - 1

BM = 3(7) - 1

BM = 21 - 1

BM = 20