Solve 4/7x−2/7>5/7

Question

. Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

Answer 1

To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), we can follow these steps:

1. Add \( \frac{2}{7} \) to both sides:
   \[ \frac{4}{7}x - \frac{2}{7} + \frac{2}{7} > \frac{5}{7} + \frac{2}{7} \] This simplifies to: \[ \frac{4}{7}x > \frac{7}{7} \]

2. Simplify \( \frac{7}{7} \):
   \[ \frac{4}{7}x > 1 \]

3. Multiply both sides by \( \frac{7}{4} \) to isolate \( x \) (note that since \( \frac{7}{4} > 0 \), the direction of the inequality does not change):
   \[ x > 1 \cdot \frac{7}{4} \]

4. Calculate \( 1 \cdot \frac{7}{4} \):
   \[ x > \frac{7}{4} \]

5. Convert \( \frac{7}{4} \) into a mixed number:
   \(\frac{7}{4} = 1 \frac{3}{4}\)

Putting it all together, the final answer in the required format is:

\[ x > 1 \frac{3}{4} \]