Question

directions: use this information to answer parts a and b. \\( 9r - \frac{3}{5} > 3\frac{9}{10} \\) \
part a \
solve the inequality by entering the correct answer in the box. \
show hints \
solution: \
(text box for solution)

Explanation:

Step1: Add $\frac{3}{5}$ to both sides

To isolate the term with \( r \), we add \(\frac{3}{5}\) to both sides of the inequality \( 9r - \frac{3}{5} > 3\frac{9}{10} \). First, convert \( 3\frac{9}{10} \) to an improper fraction: \( 3\frac{9}{10}=\frac{3\times10 + 9}{10}=\frac{39}{10} \), and \(\frac{3}{5}=\frac{6}{10}\). So the inequality becomes \( 9r> \frac{39}{10}+\frac{6}{10} \).

Step2: Simplify the right - hand side

Simplify \(\frac{39}{10}+\frac{6}{10}=\frac{39 + 6}{10}=\frac{45}{10}=\frac{9}{2}\). Now our inequality is \( 9r>\frac{9}{2} \).

Step3: Divide both sides by 9

Divide both sides of the inequality \( 9r>\frac{9}{2} \) by 9. When we divide a fraction by an integer, we multiply the fraction by the reciprocal of the integer. So \( r>\frac{9}{2}\div9=\frac{9}{2}\times\frac{1}{9}=\frac{1}{2} \).

Answer:

\( r > \frac{1}{2} \)