Solve 4/7 x − 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.

(1 point)

Answer 1

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

1. Start by isolating \( \frac{4}{7} x \): \[ \frac{4}{7} x - \frac{2}{7} + \frac{2}{7} > \frac{5}{7} + \frac{2}{7} \] This simplifies to: \[ \frac{4}{7} x > \frac{7}{7} \] which simplifies to: \[ \frac{4}{7} x > 1 \]

2. Now, multiply both sides by the reciprocal of \( \frac{4}{7} \), which is \( \frac{7}{4} \): \[ x > 1 \cdot \frac{7}{4} \] This gives us: \[ x > \frac{7}{4} \]

3. Now, convert \( \frac{7}{4} \) to a mixed number. Since \( 7 \div 4 = 1\) with a remainder of \( 3 \), we can write: \[ \frac{7}{4} = 1 \frac{3}{4} \]

Putting this all together, we write the final inequality with \( x \) first: \[ x > 1 \frac{3}{4} \]

That's the solution to the inequality.