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

Question

_____>5/7
.(1 point)
Responses

17/8
Start Fraction 17 over 8 End Fraction

4/5
Start Fraction 4 over 5 End Fraction

3/3
Start Fraction 3 over 3 End Fraction

4/9

Answer 1

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

Dividing both sides of the inequality by \( \frac{5}{7} \), we need to remember that dividing by a positive number does not change the inequality sign:

\[ x > 1 \]

Now we can evaluate the options you provided:

1. \( \frac{17}{8} \): This is greater than 1 (since \( 17 \div 8 = 2.125 \)).
2. \( \frac{4}{5} \): This is less than 1 (since \( 4 \div 5 = 0.8 \)).
3. \( \frac{3}{3} \): This equals 1 (since \( 3 \div 3 = 1 \)).
4. \( \frac{4}{9} \): This is also less than 1 (since \( 4 \div 9 \approx 0.444 \)).

The only option that satisfies the inequality \( x > 1 \) is:

\( \frac{17}{8} \).