Question

A is the midpoint of JM . If JA = 6x - 4 and JM = 9x + 13, find AM.
The length of AM is

Answer 1

`38 = AM`

Explanation:

Since A is the MIDPOINT of JM, AM is equivalent to JA, therefore you double up 6x - 4 and set that equal JM at 9x + 13:

`9x + 13 = 2[6x - 4] \\ \\ 9x + 13 = 12x - 8`

-12x - 12x

______________________

−3x + 13 = −8

- 13 - 13

______________

−3x = −21

____ ____

−3 −3

`7 = x`

[Plug this back into the equation of 6x - 4 to get the length of 38]

I am joyous to assist you anytime.

Answer 2

AM = 38

Explanation:

Since A is the midpoint of JM, then

JA = AM = 6x - 4 , and

JA + AM = JM ← substitute values

6x - 4 + 6x - 4 = 9x + 13, that is

12x - 8 = 9x + 13 ( subtract 9x from both sides )

3x - 8 = 13 ( add 8 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Hence

AM = 6x - 4 = (6 × 7) - 4 = 42 - 4 = 38