Which number would make this statement true? 5/7⋅

Question

_____ >5/7
.(1 point)
Responses
4/9
Start Fraction 4 over 9 End Fraction

3/3
Start Fraction 3 over 3 End Fraction

17/8
Start Fraction 17 over 8 End Fraction

4/5

Answer 1

To determine which number would make the inequality \( \frac{5}{7} \cdot x > \frac{5}{7} \) true, we can simplify the inequality.

1. Start with the inequality: \[ \frac{5}{7} \cdot x > \frac{5}{7} \]

2. To isolate \( x \), we can divide both sides by \( \frac{5}{7} \) (noting that since \( \frac{5}{7} > 0 \), the inequality doesn't change direction): \[ x > 1 \]

Now we need to evaluate the options given:

• \( \frac{4}{9} \) (which is less than 1)
• \( \frac{3}{3} = 1 \)
• \( \frac{17}{8} \) (which is greater than 1)
• \( \frac{4}{5} \) (which is less than 1)

The only option that satisfies the inequality \( x > 1 \) is \( \frac{17}{8} \).

Thus, the correct answer is:

17/8