In which of the following sets of numbers are all the numbers solutions to 60/g>3×5 ? (1 point)

Question

Responses

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

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

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

3, 4, and 5

Answer 1

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

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

2. Rewrite the inequality: \[ \frac{60}{g} > 15 \]

3. Next, we can manipulate the inequality by multiplying both sides by \( g \) (assuming \( g > 0 \)): \[ 60 > 15g \]

4. Divide both sides by 15: \[ \frac{60}{15} > g \] \[ 4 > g \] or equivalently, \[ g < 4 \]

Now we need to evaluate the sets of numbers:

1. Set 1: 2, 3, and 4

   • \( 2 < 4 \) ✓
   • \( 3 < 4 \) ✓
   • \( 4 < 4 \) ✗ (not valid)

2. Set 2: 1, 2, and 3

   • \( 1 < 4 \) ✓
   • \( 2 < 4 \) ✓
   • \( 3 < 4 \) ✓

3. Set 3: 4, 5, and 6

   • \( 4 < 4 \) ✗ (not valid)
   • \( 5 < 4 \) ✗ (not valid)
   • \( 6 < 4 \) ✗ (not valid)

4. Set 4: 3, 4, and 5

   • \( 3 < 4 \) ✓
   • \( 4 < 4 \) ✗ (not valid)
   • \( 5 < 4 \) ✗ (not valid)

Based on this evaluation, the only valid set where all numbers satisfy the condition \( g < 4 \) is Set 2: 1, 2, and 3.

So the answer is 1, 2, and 3.