Solve 4/7x - 2/7 > 5/7 Write the rational number in ur answer as a mized number. Make sure to write ur inequality so that x comes first

Answer 1

To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), we will first isolate the term involving \( x \) and then solve for \( x \).

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

2. Simplify the right side: \[ \frac{5}{7} + \frac{2}{7} = \frac{7}{7} = 1 \] So we have: \[ \frac{4}{7}x > 1 \]

3. Now multiply both sides by \( \frac{7}{4} \) to solve for \( x \) (noting that since \( \frac{7}{4} \) is a positive number, the direction of the inequality remains the same): \[ x > 1 \cdot \frac{7}{4} \]

4. Simplifying further: \[ x > \frac{7}{4} \]

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

Thus, the final answer, with \( x \) first, is: \[ x > 1 \frac{3}{4} \]