M is the midpoint of LN. If MN = 4x + 6 and LN = 5x + 16, what is LN?

Question

I'm having trouble on this problem on my geometry!

Answer 1

Since M is the midpoint, it divides the segment LN into 2 equal parts. That means MN = 1/2 LN (or LN = 2 MN).

You have algebraic expressions for the length of MN and LN, so substitute those expressions and solve for x:

5x+16 = 2 (4x +6).

Solve that equation for x, then substitute that value into the expression for the measure of LN to get the final answer.