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

2, 3, and 4
2, 3, and 4

1, 2, and 3

Answer 1

To determine which set of numbers are all solutions to the inequality \( 60g > 3 \times 5 \), we first need to simplify the inequality.

1. Calculate \( 3 \times 5 \): \[ 3 \times 5 = 15 \]

2. Now, the inequality becomes: \[ 60g > 15 \]

3. To isolate \( g \), divide both sides by 60: \[ g > \frac{15}{60} \]

4. Simplifying \( \frac{15}{60} \): \[ \frac{15}{60} = \frac{1}{4} \]

So, the inequality simplifies to: \[ g > \frac{1}{4} \]

Next, we check each set of numbers to see which one contains only values of \( g \) that are greater than \( \frac{1}{4} \):

1. Set: 3, 4, and 5
   All these numbers are greater than \( \frac{1}{4} \).

2. Set: 4, 5, and 6
   All these numbers are greater than \( \frac{1}{4} \).

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

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

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

Therefore, each of the provided sets of numbers are solutions:

• 3, 4, and 5: Yes
• 4, 5, and 6: Yes
• 2, 3, and 4: Yes
• 1, 2, and 3: Yes

If you must select only one that contains only values greater than \( \frac{1}{4} \), you may select any of them since all entries are valid solutions.