Question

Which value would make the statement true?

StartFraction 2 Over question mark EndFraction greater-than StartFraction 4 Over 12 EndFraction
4
6
12
2

Answer 1

To determine which value makes the statement true, we need to find a value for the question mark (let's call it \( x \)) such that:

\[
\frac{2}{x} > \frac{4}{12}
\]

First, we simplify the right side:

\[
\frac{4}{12} = \frac{1}{3}
\]

Now we have:

\[
\frac{2}{x} > \frac{1}{3}
\]

To solve for \( x \), we can cross-multiply (noting that \( x \) must be positive to avoid flipping the inequality):

\[
2 \cdot 3 > 1 \cdot x
\]

This simplifies to:

\[
6 > x
\]

or

\[
x < 6
\]

Now, let's evaluate the options given:

- \( 4 \): \( 4 < 6 \) (True)
- \( 6 \): \( 6 < 6 \) (False)
- \( 12 \): \( 12 < 6 \) (False)
- \( 2 \): \( 2 < 6 \) (True)

The values that satisfy the inequality \( x < 6 \) are \( 4 \) and \( 2 \). Therefore, the values that would make the original statement true are \( 4 \) and \( 2 \). Among the options provided, both are valid answers. If only one value is to be selected, \( 4 \) is the highest possible choice satisfying the condition.