Answer:
The value of BC is 30.
Step-by-step explanation:
Given information: A, B, and C are collinear, B lies between A and C, AC = 48, AB = 2x+2, and BC = 3x+6.
If A, B, and C are collinear, B lies between A and C, then by using segment addition property, we get
![AB+BC=AC](https://tex.z-dn.net/?f=AB%2BBC%3DAC)
Substitute AC = 48, AB = 2x+2, and BC = 3x+6 in the above equation.
![(2x+2)+(3x+6)=48](https://tex.z-dn.net/?f=%282x%2B2%29%2B%283x%2B6%29%3D48)
On combining like terms we get
![(2x+3x)+(2+6)=48](https://tex.z-dn.net/?f=%282x%2B3x%29%2B%282%2B6%29%3D48)
![5x+8=48](https://tex.z-dn.net/?f=5x%2B8%3D48)
Subtract 8 from both sides.
![5x=48-8](https://tex.z-dn.net/?f=5x%3D48-8)
![5x=40](https://tex.z-dn.net/?f=5x%3D40)
Divide 5 from both sides.
![x=8](https://tex.z-dn.net/?f=x%3D8)
The value of x is 8.
We need to find the value of BC.
![BC=3x+6\Rightarrow 3(8)+6=30](https://tex.z-dn.net/?f=BC%3D3x%2B6%5CRightarrow%203%288%29%2B6%3D30)
Therefore the value of BC is 30.