Question

find the value of x.
x = ?

Explanation:

Step1: Use similar - triangle property

Since $DE\parallel AC$, $\triangle BDE\sim\triangle BAC$. Then $\frac{BD}{BA}=\frac{BE}{BC}$.
We know $BD = 6$, $BA=6 + 4=10$, $BE=x + 1$, and $BC=(x + 1)+x=2x + 1$. So $\frac{6}{10}=\frac{x + 1}{2x+1}$.

Step2: Cross - multiply

$6(2x + 1)=10(x + 1)$.
Expand: $12x+6 = 10x + 10$.

Step3: Solve for x

$12x-10x=10 - 6$.
$2x=4$, so $x = 2$.

Answer:

$2$