Given the line segment NK
As shown:
[tex]\begin{gathered} NK=x+243 \\ NM=110+4x \\ ML=x+103 \\ LK=70 \end{gathered}[/tex]
All the points are collinear:
So,
[tex]NK=NM+ML+LK[/tex]
substitute with the values of each term
so,
[tex]x+243=(110+4x)+(x+103)+70[/tex]
solve the equation to find x:
Combine the like terms:
[tex]\begin{gathered} x-4x-x=110+103+70-243 \\ -4x=283-243 \\ -4x=40 \\ x=\frac{40}{-4}=-10 \end{gathered}[/tex]
now, substitute with x into the equation of ML
so,
[tex]ML=x+103=-10+103=93[/tex]
so, the answer will be:
[tex]ML=93[/tex]
