Question

Which of the following are solutions to the inequality below? Select all that apply.

24 >
d
5
D=60 d=40 d=55 d=115

Answer 1

We need to solve the inequality \( \frac{24}{d} > 5 \).

First, we can rewrite the inequality:

\[
\frac{24}{d} > 5
\]

To eliminate the fraction, we can multiply both sides by \( d \), but we must consider that multiplying or dividing by a negative number will reverse the inequality. Therefore, we need to analyze two cases: \( d > 0 \) and \( d < 0 \).

1. Assume \( d > 0 \):

\[
24 > 5d
\]

Dividing both sides by 5:

\[
\frac{24}{5} > d
\]

Therefore:

\[
d < \frac{24}{5} \quad (4.8)
\]

2. Assume \( d < 0 \):
Since \( d \) is in the denominator and if \( d < 0 \), the left side will be negative and the inequality cannot hold as \( 24 \) is positive.

Thus, \( d \) must be a positive number less than \( 4.8 \).

Now, let's check the given values:

- \( d = 60 \): This is greater than \( 4.8 \) (not a solution).
- \( d = 40 \): This is greater than \( 4.8 \) (not a solution).
- \( d = 55 \): This is greater than \( 4.8 \) (not a solution).
- \( d = 115 \): This is greater than \( 4.8 \) (not a solution).

None of the provided values satisfy the inequality \( d < 4.8 \).

**So, there are no solutions from the given options.**