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.