To solve the inequality \(\frac{4}{7}x - \frac{2}{7} > \frac{5}{7}\), we need to isolate \(x\).
First, we can move the \(\frac{2}{7}\) to the right side by adding it to both sides of the inequality:
\(\frac{4}{7}x > \frac{5}{7} + \frac{2}{7}\)
Simplifying the right side:
\(\frac{4}{7}x > \frac{7}{7}\)
\(\frac{4}{7}x > 1\)
Next, we can multiply both sides of the inequality by \(\frac{7}{4}\) (the reciprocal of \(\frac{4}{7}\)) to solve for \(x\). However, since we want \(x\) to be in simplified mixed number form, we can rearrange the inequality and solve it in that form.
\(\frac{4}{7}x > 1\)
\(x > \frac{7}{4}\)
The mixed number form of \(\frac{7}{4}\) is \(1 \frac{3}{4}\).
Therefore, the solution to the inequality in mixed number form is \(x > 1 \frac{3}{4}\).
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.
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