If C is between A and B, then, we can write the equation
[tex]AB = AC + CB[/tex]
Substitute the value of AB and the expressions for AC and CB in terms of x.
[tex]40 = (2x+10)+(3x-5)[/tex]
We can now solve for x.
[tex]40-10+5= 2x+3x[/tex]
[tex]35=5x[/tex]
Dividing by 5.
[tex]7=x[/tex]
[tex]AB=40[/tex]
[tex]AC=2(7)+10[/tex]
[tex]AC=14+10[/tex]
[tex]AC=24[/tex]
[tex]BC=3(7)-5[/tex]
[tex]BC=21-5[/tex]
[tex]BC=16[/tex]
