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

Answer 1

To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), we start by isolating \( x \) on one side.

1. First, add \( \frac{2}{7} \) to both sides: \[ \frac{4}{7}x > \frac{5}{7} + \frac{2}{7} \] This simplifies to: \[ \frac{4}{7}x > \frac{7}{7} \] Since \( \frac{7}{7} = 1 \), we rewrite the inequality as: \[ \frac{4}{7}x > 1 \]

2. Next, multiply both sides by \( \frac{7}{4} \) to isolate \( x \). Remember, since \( \frac{7}{4} \) is positive, the direction of the inequality does not change: \[ x > 1 \cdot \frac{7}{4} \] This simplifies to: \[ x > \frac{7}{4} \]

3. Now, we need to express \( \frac{7}{4} \) as a mixed number. To convert it:

   • Divide 7 by 4, which gives you 1 with a remainder of 3. Thus, \[ \frac{7}{4} = 1 \frac{3}{4} \]

Finally, the solution to the inequality is: \[ x > 1 \frac{3}{4} \]

Make sure your inequality is written with \( x \) first: \[ x > 1 \frac{3}{4} \]