Question

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.

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

(1 point)

Answer 1

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

1. Add \(\frac{2}{7}\) to both sides:

\[
\frac{4}{7}x > \frac{5}{7} + \frac{2}{7}
\]

2. Combine the right side:

\[
\frac{4}{7}x > \frac{7}{7}
\]

This simplifies to:

\[
\frac{4}{7}x > 1
\]

3. Now, to isolate \( x \), multiply both sides by the reciprocal of \(\frac{4}{7}\), which is \(\frac{7}{4}\):

\[
x > 1 \cdot \frac{7}{4}
\]

4. This gives us:

\[
x > \frac{7}{4}
\]

5. Now, convert \(\frac{7}{4}\) to a mixed number. Divide 7 by 4:

\[
7 \div 4 = 1 \quad \text{remainder} \quad 3
\]

So, \(\frac{7}{4} = 1\frac{3}{4}\).

Thus, the final inequality is:

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

Therefore, the answer is:

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