Let's start solving this problem step by step.
Step 1:
First, we have the equation km = 2x − 17, which states that km is equal to twice a certain variable x, subtracted by 17.
Step 2:
The second equation provided is km = kl + lm. We know that kl equals 15, so we can substitute kl in our second formula to get km = 15 + lm.
Step 3:
Now we have two expressions for km. We can set these equal to solve for x:
2x - 17 = 15 + lm
Step 4:
Solving this equation for x, we find that x = 0.5km + 8.5
Step 5:
Next, if we recall the initial condition lm = x − 13, substituting 0.5km + 8.5 for x gives us:
lm = 0.5km + 8.5 - 13 = 0.5km - 4.5
Hence, we arrive at the length of lm = 0.5km - 4.5. This is the conclusion of the problem !