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.
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(1 point)
whats the answer
??
To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), first add \( \frac{2}{7} \) to both sides to isolate the term with the variable x on one side:
\( \frac{4}{7}x - \frac{2}{7} + \frac{2}{7} > \frac{5}{7} + \frac{2}{7} \)
\( \frac{4}{7}x > \frac{7}{7} \)
Now that we have \( \frac{7}{7} \) on the right side, we know that \( \frac{7}{7} \) is equal to 1 because it's a fraction representing a whole. So the inequality now looks like:
\( \frac{4}{7}x > 1 \)
To solve for x, we multiply both sides by the reciprocal of \( \frac{4}{7} \), which is \( \frac{7}{4} \), to get x alone:
\( \frac{7}{4} \cdot \frac{4}{7}x > 1 \cdot \frac{7}{4} \)
\( x > \frac{7}{4} \)
The fraction \( \frac{7}{4} \) can be written as a mixed number because 7 divided by 4 is 1 with a remainder of 3. Hence:
\( x > 1\frac{3}{4} \)
Rearranging the inequality to have x come first:
\( x > 1\frac{3}{4} \)
So the solution to the inequality is:
\( x > 1\frac{3}{4} \)