Answer:
x = 2
Step-by-step explanation:
Basic proportionality theorem,
[tex]\frac{AB}{BD}=\frac{CB}{BE}\\[/tex]
AB = AD + DB = 4+6 = 10
CB = CE + EB = x + x +1 = 2x +1
[tex]\frac{10}{6}=\frac{2x+1}{x+1}[/tex]
Cross multiply
10*(x+1) = 6*(2x+ 1)
10*x + 10*x = 6*2x + 6*1
10x + 10 = 12x + 6
Subtract 10x from both sides
10x + 10 - 10x = 12x + 6 - 10x
10 = 2x + 6
Subtract 6 form both sides
10 - 6 = 2x + 6 - 6
4 = 2x
Divide both sides by 2
4/2 = 2x/2
2 = x
x = 2
