Answer:
[tex]ML=27\\LN=27\\MN=54[/tex]
Step-by-step explanation:
Since L is the midpoint of MN, by the definition of midpoint:
[tex]ML=LN[/tex]
We can picture the following segment:
M----------L----------N
We know that [tex]ML=2x+7[/tex] and [tex]LN=3x-3[/tex]. Since the two segments are equivalent, we can set them equal to each other:
[tex]2x+7=3x-3[/tex]
Now, let's solve for x. Subtract -7 from both sides:
[tex]2x=3x-10[/tex]
Subtract 3x from both sides:
[tex]-x=-10[/tex]
Divide both sides by -1:
[tex]x=10[/tex]
So, the value of x is 10.
With this, we can find the remaining lengths.
We know that ML is [tex]2x+7[/tex].
Substitute 10 for x. So, the length of ML is:
[tex]ML=2(10)+7=20+7=27[/tex]
We know that LN is [tex]3x-3[/tex]. So, the length of LN is:
[tex]LN=3(10)-3=30-3=27[/tex]
Finally, MN will be the combined lengths of ML and LN. So:
[tex]MN=ML+LN=27+27=54[/tex]
And we're done!
