Answer:
The value of AM = 43
Step-by-step explanation:
As point M is the midpoint of AB, so
Given
AB = 8x - 50
AM = 2x + 9
so substituting AB = 8x - 50 and AM = 2x + 9 in the equation AB = AM + BM
AB = AM + BM
8x - 50 = 2x + 9 + BM
8x - 2x - 50 - 9 = BM
6x - 50 = BM
Thus,
BM = 6x - 59
As
AM = BM
so substituting AM = 2x + 9 and BM = 6x - 59 in the equation AM = BM
2x + 9 = 6x - 59
switch sides
6x - 59 = 2x + 9
subtract 2x from both sides
6x - 2x - 59 = 2x + 9 - 2x
4x - 59 = 9
add 59 to both sides
4x - 59 + 59 = 9 + 59
4x = 68
divide both sides by 4
4x/4 = 68/4
x = 17
Thus, the value of x = 17
Therefore, the value of AM will be:
AM = 2x + 9 = 2(17) + 9 = 34 + 9 = 43
Hence, the value of AM = 43
Verification:
AM = BM
2x + 9 = 6x - 59
2(17) + 9 = 6(17) - 59
34 + 9 = 102 - 59
43 = 43
and
AB = 8x - 50 = 8(17) - 50 = 86
