Question

Find AC, CB, and AB.AC =2x+1CB = 3x-4AC = CB

Answer 1

We have from the picture:

`AC=2x+1,CB=3x-4`
`AC=CB\rightarrow2x+1=3x-4`

We need to solve both equations for x:

`2x+1=3x-4\rightarrow4+1=3x-2x\rightarrow5=x\rightarrow x=5`

In the first case, we subtract 2x to both sides of the equation. And then we add 4 to both sides of the equation.

`2x-2x+4+1=3x-2x-4+4`
`0+5=x+0\rightarrow x=5`

Then,

`AC=2x+1=2\cdot(5)+1=10+1=11\rightarrow AC=11`
`CB=3x-4=3\cdot(5)-4=15-4=11\rightarrow CB=11`
`AB=AC+CB=11+11=22\rightarrow AB=22`

Therefore, AC = 11, CB = 11, and AB = 22.