Given $x\le 5$ and $y>5$. I want to minimize th function $|1-1.1y+0.8x|$.

By trial my assumption is $|1-1.1y+0.8x|>0.5$. But I am unable to prove this.

If I'm right then how to prove this ? If I'm wrong then what will be the minimum value ?

Any help plase ?