We know that points A, B and C are collinear, this mean that they are located on the same line. We are given an expression for AB and BC and the measure of AC.
Then we have:
The sum of AB and BC is 48.
[tex]AB+BC=48[/tex]
We replace the expression:
[tex](2x+2)+(3x+6)=48[/tex]
Now we solve for x:
[tex]\begin{gathered} 2x+2+3x+6=48 \\ 2x+3x=48-2-6 \\ 5x=40 \\ x=\frac{40}{5}=8 \end{gathered}[/tex]
Now that we have the value of x, we can replace it in the expression for BC.
[tex]\begin{gathered} BC=3x+6 \\ BC=3\cdot8+6 \\ BC=30 \end{gathered}[/tex]
