Point M is on line segment LN. Given MN = 3x, LN = 4x + 9, and LM = 2x + 7,

Question

determine the numerical length of LM.

Answer 1

Since M is on the line segment LN, we have the equation MN + LM = LN.
Substituting the given values, we get 3x + (2x + 7) = 4x + 9
Combining like terms, we have 5x + 7 = 4x + 9
Subtracting 4x and 7 from both sides, we get x = 2
Substituting x = 2 back into the equation for LM, we get LM = 2(2) + 7 = 4 + 7 = 11
Therefore, the numerical length of LM is 11. Answer: \boxed{11}.