Question

Point M is the midpoint of the line segment LN. LM=8x+2 and MN=10x-4 solve for x and find the length is segment LM

Answer 1

x = 3

`LM = 26`

Explanation:

Given:

`LM = 8x + 2`

`MN = 10x - 4`

Required:

Value of x and length of segment LM

SOLUTION:

Since M is the midpoint of line segment LN, it implies that:

`LM = MN`

`8x + 2 = 10x - 4` (substitution)

Combine like terms

`2 + 4 = 10x - 8x`

`6 = 2x`

Divide both sides by 2

`(6)/(2) = (2x)/(2)`

`3 = x`

`x = 3`

`LM = 8x + 2`

Plug in the value of x

`LM = 8(3) + 2`

`LM = 24 + 2`

`LM = 26`