How do I solve this problem?

Point P is between points L and M. LM = 10x, LP = 2x + 4, and PM = 3x + 16. Solve for x.

2x + 4 + 3x + 16 = 10x

Solve for x.

To solve this problem, we can use the fact that the sum of the lengths of the two segments that compose a line should be equal to the length of the whole line.

In this case, we have that LP + PM should be equal to LM.

LP + PM = LM

Substituting the given values:

(2x + 4) + (3x + 16) = 10x

Now, we can solve for x by simplifying and solving the resulting equation:

2x + 4 + 3x + 16 = 10x

Combine like terms:

5x + 20 = 10x

Subtract 5x from both sides:

20 = 5x

Divide both sides by 5:

20/5 = x

x = 4

Therefore, x = 4 is the solution to the problem.