Given:
Midpoint of LN = M
LM = 5x - 10
MN = 2x + 2
Since M is the midpoint of LN, it means that M divides LN by 2 equal sides.
It is represented graphically as:
Since LM and MN are equal, We have:
LM = MN
5x - 10 = 2x + 2
Let's solve for x.
Add 10 t0 both sides:
5x - 10 + 10 = 2x + 2 + 10
5x = 2x + 12
Subtract 2x from both sides:
5x - 2x = 2x - 2x + 12
3x = 12
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Input 4 for x to find LM and MN.
LM = 5x - 10
= 5(4) - 10
= 20 - 10
= 10
MN = 2x + 2
= 2(4) + 2
= 8 + 2
= 10
LN = LM + MN
= 10 + 10
= 20
ANSWER:
LN = 20
