Question

The product of 8 and a number k is greater than 4 and no more than 16

Answer 1

We can express the given condition mathematically as follows:

\[
4 < 8k \leq 16
\]

To solve this compound inequality, we will break it down into two parts:

1. **First part**: \( 8k > 4 \)

To isolate \( k \), divide both sides by 8:
\[
k > \frac{4}{8} = \frac{1}{2}
\]

2. **Second part**: \( 8k \leq 16 \)

Again, divide both sides by 8:
\[
k \leq \frac{16}{8} = 2
\]

Now, we can combine the results of both parts:

\[
\frac{1}{2} < k \leq 2
\]

Thus, the range for \( k \) is:

\[
k \in \left( \frac{1}{2}, 2 \right]
\]

This means \( k \) must be greater than \( \frac{1}{2} \) and less than or equal to \( 2 \).