In which of the following sets of numbers are all the numbers solutions to 60g>3×5

Question

?(1 point)
Responses

3, 4, and 5
3, 4, and 5

4, 5, and 6
4, 5, and 6

1, 2, and 3
1, 2, and 3

2, 3, and 4
2, 3, and 4
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Answer 1

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

\[ 3 \times 5 = 15 \]

Now, our inequality becomes:

\[ 60g > 15 \]

Next, we divide both sides of the inequality by 60:

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

Simplifying \(\frac{15}{60}\):

\[ \frac{15}{60} = \frac{1}{4} \]

Thus, the solution to the inequality is:

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

Now we need to check each response set to see which numbers are greater than \(\frac{1}{4}\):

1. Set: 3, 4, and 5

   • All of these numbers are greater than \(\frac{1}{4}\).

2. Set: 4, 5, and 6

   • All of these numbers are greater than \(\frac{1}{4}\).

3. Set: 1, 2, and 3

   • All of these numbers (1, 2, and 3) are also greater than \(\frac{1}{4}\).

4. Set: 2, 3, and 4

   • All of these numbers (2, 3, and 4) are greater than \(\frac{1}{4}\).

Since all sets have their numbers greater than \(\frac{1}{4}\), they are all solutions to the inequality \( 60g > 15 \).

If you need to select one correct response, any of the provided options would be valid as they all contain numbers that satisfy the inequality.