This is in general not true. Think about the case where $Z$ is negative, then this does not hold true:
$$\text{if} x \leq Z, \text{then} xZ \leq tZ$$
Question
I have an algorithm that has the following cost:
C(Alg) <= t * Z
I've found on the web an exercise that state the following :
if t>=x, I can say that C(Alg) <= x * Z <= t * Z
but it looks strange.. do you agree?
Solution
This is in general not true. Think about the case where $Z$ is negative, then this does not hold true:
$$\text{if} x \leq Z, \text{then} xZ \leq tZ$$