Question

Point M is on line segment start overline, L, N, end overline

LN
. Given L, N, equals, 2, x, minus, 5, commaLN=2x−5, M, N, equals, x, minus, 1, commaMN=x−1, and L, M, equals, 3, commaLM=3, determine the numerical length of start overline, L, N, end overline, .
LN
.

Answer 1

LN = 9

Explanation:

given point M is on line segment LN , then

LN = LM + MN ( substitute values )

2x - 5 = 3 + x - 1 ( simplify right side )

2x - 5 = x + 2 ( subtract x from both sides )

2x - x - 5 = x - x + 2 ( simplify both sides )

x - 5 = 2 ( add 5 to both sides )

x - 5 + 5 = 2 + 5 ( simplify both sides )

x = 7

Then

LN = 2x - 5 = 2(7) - 5 = 14 - 5 = 9