At which value of $x$ is $f(x) = \lvert 2x - 5 \rvert$ not differentiable?

Explanation

1. 01

   A modulus has its corner where its inside is 0.

2. 02

   $2x - 5 = 0$ at $x = \frac{5}{2}$; there the slope changes from $-2$ to 2.