We have from the picture:
[tex]AC=2x+1,CB=3x-4[/tex][tex]AC=CB\rightarrow2x+1=3x-4[/tex]We need to solve both equations for x:
[tex]2x+1=3x-4\rightarrow4+1=3x-2x\rightarrow5=x\rightarrow x=5[/tex]In the first case, we subtract 2x to both sides of the equation. And then we add 4 to both sides of the equation.
[tex]2x-2x+4+1=3x-2x-4+4[/tex][tex]0+5=x+0\rightarrow x=5[/tex]Then,
[tex]AC=2x+1=2\cdot(5)+1=10+1=11\rightarrow AC=11[/tex][tex]CB=3x-4=3\cdot(5)-4=15-4=11\rightarrow CB=11[/tex][tex]AB=AC+CB=11+11=22\rightarrow AB=22[/tex]Therefore, AC = 11, CB = 11, and AB = 22.
