Question

Solve the inequality.
1. - z/5 greater than or equal to 4
2. -4n greater than or equal to 14

Answer 1

Let's solve the inequalities one by one.

### 1. Solve the inequality \(-\frac{z}{5} \geq 4\)

To isolate \(z\), we can first multiply both sides of the inequality by \(-5\). Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign.

\[
-\frac{z}{5} \geq 4 \implies z \leq 4 \times (-5)
\]

Calculating the right side:

\[
z \leq -20
\]

So, the solution for the first inequality is:

\[
z \leq -20
\]

### 2. Solve the inequality \(-4n \geq 14\)

Again, we need to isolate \(n\). We will start by dividing both sides by \(-4\). Remember, just like before, to reverse the inequality sign because we are dividing by a negative number.

\[
-4n \geq 14 \implies n \leq \frac{14}{-4}
\]

Calculating the right side:

\[
n \leq -\frac{14}{4} = -\frac{7}{2} = -3.5
\]

So, the solution for the second inequality is:

\[
n \leq -3.5
\]

### Summary:
1. \(z \leq -20\)
2. \(n \leq -3.5\)