Question

Solve Inequalities Quick Check 5 of 55 of 5 Items Question In which of the following sets of numbers are all the numbers solutions to 60g>3×5 ? Responses 1, 2, and 3 1, 2, and 3 - no response given 4, 5, and 6 4, 5, and 6 - no response given 3, 4, and 5 3, 4, and 5 - no response given 2, 3, and 4

Answer 1

To solve the inequality \(60g > 3 \times 5\), we first simplify the right side:

\[
3 \times 5 = 15
\]

So we have:

\[
60g > 15
\]

Next, we divide both sides by 60 to isolate \(g\):

\[
g > \frac{15}{60}
\]

This simplifies to:

\[
g > \frac{1}{4}
\]

Now we need to determine which of the provided sets of numbers contain only solutions where \(g > \frac{1}{4}\).

Let's evaluate each possible option based on a possible set of numbers (let's assume each option corresponds to some hypothetical numbers):

- **Option 1 (1, 2, and 3)**: All numbers are less than \(1/4\), so none are solutions.
- **Option 2 (4, 5, and 6)**: All numbers are greater than \(1/4\), so all are solutions.
- **Option 3 (3, 4, and 5)**: Check these numbers one by one:
- 3 is not greater than \(1/4\).
- 4 is greater than \(1/4\).
- 5 is greater than \(1/4\).
- **Option 4 (2, 3, and 4)**: 2 and 4 are greater than \(1/4\), but 3 is not.

From this analysis, the option where all values are solutions (\(g > \frac{1}{4}\)) is:

**4, 5, and 6**.

Thus, the correct answer is: **4, 5, and 6**.