Since we have
[tex] \overline{AB}+\overline{BC}=\overline{AC} [/tex]
let's plug the value for each segment measure in the formula:
[tex] 5x + 11x-5 = 75 [/tex]
The left hand side evaluates to
[tex] 16x-5 = 75 [/tex]
Add 5 to both sides:
[tex] 16x = 80 [/tex]
Divide both sides by 16:
[tex] x = \dfrac{80}{16} = 5 [/tex]
Now that we know the value for x, we can plug it in the expressions for both segments:
[tex] \overline{AB} = 5x=5\cdot 5 = 25 [/tex]
[tex] \overline{BC} = 11x-5=11\cdot 5-5 = 55-5=50 [/tex]
