Question
Solve the inequality $-25 z \leq 2$, and write the solution in interval notation.
Answer
Final Answer: The solution to the inequality \(-25z \leq 2\) in interval notation is \(\boxed{[-0.08, \infty)}\).
Step 1 ：The inequality is \(-25z \leq 2\). To solve for \(z\), we need to divide both sides of the inequality by \(-25\). However, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So, we should end up with \(z \geq -\frac{2}{25}\).
Step 2 ：The value of \(z\) is calculated as \(-0.08\).
Step 3 ：Since \(z\) is greater than or equal to \(-0.08\), the interval notation for this solution is \([-0.08, \infty)\).
Step 4 ：Final Answer: The solution to the inequality \(-25z \leq 2\) in interval notation is \(\boxed{[-0.08, \infty)}\).
