Question

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

4 5 6
2 3 4
1 2 3
3 4 5

Answer 1

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

\[
3 \times 5 = 15
\]
So, we are solving:

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

Next, we multiply both sides by \( g \) (assuming \( g > 0 \) to avoid division by zero and to keep the inequality direction unchanged):

\[
60 > 15g
\]

Now, divide both sides by 15:

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

This simplifies to:

\[
4 > g \quad \text{or} \quad g < 4
\]

Now we check the provided sets of numbers to see which values are less than 4:

1. Set \( \{4, 5, 6\} \): Contains 4, which does not satisfy \( g < 4 \) (excluded).
2. Set \( \{2, 3, 4\} \): Contains 4, which does not satisfy \( g < 4 \) (excluded).
3. Set \( \{1, 2, 3\} \): All numbers (1, 2, 3) satisfy \( g < 4 \) (included).
4. Set \( \{3, 4, 5\} \): Contains 4, which does not satisfy \( g < 4 \) (excluded).

Therefore, the only set of numbers where all the number solutions satisfy \( g < 4 \) is:

\(\{1, 2, 3\}\)