Question

Solve the inequality’s.
1. 8p less than or equal to 32
2. -k/2 < -5
3. 3/5t > -9

Answer 1

Let's solve each inequality step by step.

1. **Inequality:** \( 8p \leq 32 \)

Divide both sides by 8:
\[
p \leq \frac{32}{8}
\]
\[
p \leq 4
\]

2. **Inequality:** \( -\frac{k}{2} < -5 \)

To get rid of the negative sign, multiply both sides by -1 and reverse the inequality sign:
\[
\frac{k}{2} > 5
\]

Now, multiply both sides by 2:
\[
k > 10
\]

3. **Inequality:** \( \frac{3}{5}t > -9 \)

To isolate \( t \), multiply both sides by \( \frac{5}{3} \) (which is positive, so the inequality sign remains the same):
\[
t > -9 \cdot \frac{5}{3}
\]
\[
t > -\frac{45}{3}
\]
\[
t > -15
\]

### Summary of Solutions:
1. \( p \leq 4 \)
2. \( k > 10 \)
3. \( t > -15 \)