In the given figure, $ABC$ is a triangle in which $DE \parallel BC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$ and $EC = x - 1$, then find the value of $x$.

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Step 1: In $	riangle ABC$, $DE \parallel BC$. By BPT: $\frac{AD}{DB} = \frac{AE}{EC} \Rightarrow \frac{x}{x - 2} = \frac{x + 2}{x - 1}$.
Step 2: $x(x - 1) = (x + 2)(x - 2) \Rightarrow x^2 - x = x^2 - 4 \Rightarrow x = 4$.

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