L is the midpoint of MN¯¯¯¯¯¯¯, ML=2x+7 and LN=3x−3. Find ML, LN, and MN.

Step-by-step explanation:

Since L is the midpoint of MN, by the definition of midpoint:

We can picture the following segment:

M----------L----------N

We know that and . Since the two segments are equivalent, we can set them equal to each other:

Now, let's solve for x. Subtract -7 from both sides:

Subtract 3x from both sides:

Divide both sides by -1:

So, the value of x is 10.

With this, we can find the remaining lengths.

We know that ML is .

Substitute 10 for x. So, the length of ML is:

We know that LN is . So, the length of LN is:

Finally, MN will be the combined lengths of ML and LN. So:

And we're done!

£56

step-by-step explanation: