A manufacturing process outputs a batch of items with weight $W$ (in kilograms) such that the variance from the target weight of $10$ kg is at most $1.5$ kg. This is expressed by the inequality $|W - 10| \leq 1.5$. If a different machine produces items with a weight $W_{new} = 2W - 5$, what is the range of $W_{new}$?