Question

Which of the following is a solution to the inequality below?

–8/m ≤ –8

Answer 1

To solve the inequality \(-\frac{8}{m} \leq -8\), we can start by isolating \(m\).

Step 1: Multiply both sides by \(-1\) (remember to flip the inequality sign when multiplying by a negative number):

\[
\frac{8}{m} \geq 8
\]

Step 2: Next, we can rewrite the inequality:

\[
\frac{8}{m} \geq 8
\]

Step 3: Multiply both sides by \(m\) (note that we have to consider the sign of \(m\)):
1. If \(m > 0\):

\[
8 \geq 8m \\
1 \geq m \quad (dividing\ by\ 8)
\]

2. If \(m < 0\):

Flipping the direction of the inequality gives:

\[
8m \geq 8 \\
m \geq 1 \quad (dividing\ by\ 8)
\]

In this case, since \(m < 0\), there are no solutions.

Combining both cases, the solution to the original inequality \( -\frac{8}{m} \leq -8 \) is:

\[
m \leq 1
\]

Plus, \(m\) must be positive to maintain the equality \(-\frac{8}{m} \frac{8}{m} > 0\).

Thus, the solution is:

\[
0 < m \leq 1
\]

Examples of solutions are any values for \(m\) in the interval \((0, 1]\), such as \(0.5\), \(1\), etc.