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

Answer:

x = 3

$LM = 26$

Step-by-step 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

$\frac{6}{2} = \frac{2x}{2}$

$3 = x$

$x = 3$

$LM = 8x + 2$

Plug in the value of x

$LM = 8(3) + 2$

$LM = 24 + 2$

$LM = 26$