Question

If L-M-N, and if LM = 2x , MN = 3x - 1 , and LN = 24 , then find MN.

Answer 1

L-M-N means that point M is between points L and N.  Therefore, LM + MN = LN.

2x + (3x - 1) = 24
5x - 1 = 24
5x = 25
x = 5

Substitute into the expression for MN.  MN = 3x - 1 = 3(5) - 1 = 14.
MN =14