The value of x is 6.
Solution:
By Proportionality theorem,
If a parallel line to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
[tex]$\Rightarrow \frac{2}{3} =\frac{x}{x+3}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 2(x+3)=3x[/tex]
[tex]$\Rightarrow 2x+6=3x[/tex]
Divide by 2x on both sides of the equation.
⇒ 6 = x
⇒ x = 6
The value of x is 6.