Point M is on line segment LN. Given MN = 3x, LN = 4x + 9, and LM = 2x + 7,
determine the numerical length of LM.
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}.
To find the length of LM, we need to solve for x in the given information.
Since M is a point on line segment LN, the lengths of LM and MN should add up to the length of LN.
So, we can set up the equation:
LM + MN = LN
Substituting the given lengths, we have:
(2x + 7) + (3x) = 4x + 9
Simplifying the equation:
2x + 7 + 3x = 4x + 9
Combine like terms:
5x + 7 = 4x + 9
Subtract 4x from both sides to isolate x:
5x - 4x + 7 = 9
Simplifying:
x + 7 = 9
Subtract 7 from both sides to solve for x:
x = 2
Now that we have found the value of x, we can substitute it back into the expression for LM:
LM = 2x + 7
Substituting x = 2:
LM = (2)(2) + 7
Simplifying:
LM = 4 + 7
LM = 11
Therefore, the length of LM is 11.
To find the length of LM, we need to substitute the given values into the equation and solve for x.
We are given that MN = 3x, LN = 4x + 9, and LM = 2x + 7.
Since M is on the line segment LN, the sum of the lengths of MN and LM should be equal to the length of LN. Mathematically, it can be written as:
MN + LM = LN
Substituting the given values:
3x + (2x + 7) = 4x + 9
Now, we can solve this equation to find the value of x.
Combine like terms:
5x + 7 = 4x + 9
Subtract 4x from both sides:
5x - 4x + 7 = 9
Simplify:
x + 7 = 9
Subtract 7 from both sides:
x + 7 - 7 = 9 - 7
Simplify:
x = 2
Now that we have the value of x, we can find the numerical length of LM by substituting x into the equation:
LM = 2x + 7
LM = 2(2) + 7
LM = 4 + 7
LM = 11
Therefore, the numerical length of LM is 11.