If KL = 8x, LM = 3, and KM = x + 10, what is KM

Answer 1

Either point L is on line segment KM or else it is not. If it is, then KL + LM = KM by the line segment addition postulate.

If L is not on the line segment KM, then KL + LM = the length of the line segments from K to M going through L.

Under either of these two assumptions, we can set up the equation:

8x + 3 = x + 10

(Note that there was a small error made in translating the word problem to an equation above. Always be careful, because even the best of us can make a mistake every now and then.)

Subtract 3 from both sides:

8x = x + 7

Subtract x from both sides:

7x = 7

Divide both sides by 7:

x = 7

Check your work:

KL = 8x = 8*1 = 8

LM = 3

KM = x + 10 = 1 + 10 = 11

KL + LM = 8 + 3 = 11 = KM

And our work checks out, verifying that we have the correct answer.

Answer 2

Assuming these are points on a line

KL + LM = KM

8 + 3 = x + 10