If LM= 6x +12 , MN= 3x + 4 , and LN= 52. Find x. Then, find LM

Answer 1

This is a midpoint problem where:

LM + MN = LN

LN = 52

LM = 6x +12

MN = 3x + 4

So we can substitute the values into the top equation:

6x + 12 + 3x + 4 = 52

Now we solve for x by combining like terms:

6x + 3x + 12 + 4 = 52

9x + 16 = 52

Now subtract 16 from both sides of the equation:

9x + 16 - 16 = 52 - 16

9x = 36

Now divide both sides by 9:

9x / 9 = 36 / 9

x = 36 / 9 = 4

x = 4

But be careful because we are not finished with the problem. The directions say to find LM, so we need to put 4 in for x in the LM equation:

LM = 6x +12

LM = 6(4) +12

LM = 24 +12 = 36

LM = 36

The final answer to the question is LM = 36.

These questions with multiple parts can be a bit confusing. If you'd like to book a lesson I am happy to help you build the tools necessary to handle these problems.

Answer 2

Without a visual, I am assuming that LM + MN = LN

(6x + 12) + (3x + 4) = 52 Combine like terms

9x + 16 = 52 Subtract 16 from both sides

9x = 36 Divide both sides by 9

x = 4