Question

Point L is on line segment KM. Given LM = 3x + 3,

KM = 5x + 4, and
KL = 5x + 1, determine the numerical length of KM.

Answer: KM =

Answer 1

KM = 4

Explanation:

`LM = 3x + 3`

`KM = 5x + 4`

`KL = 5x + 1`

`KL + LM = KM` (segment addition postulate)

`(5x + 1) + (3x + 3) = 5x + 4` (substitution)

Solve for x

`5x + 1 + 3x + 3 = 5x + 4`

Combine like terms

`8x + 4 = 5x + 4`

`8x + 4 - 4 = 5x + 4 - 4`

`8x = 5x + 0`

`8x - 5x = 0`

`3x = 0`

`x = 0`

`KM = 5x + 4`

Plug in the value of x

`KM = 5(0) + 4`

`KM = 0 + 4 = 4`