5x/9 < 8. write the improper fraction in your answer as mixed number. make sure to write tour inequality so that x comes first.

Answer 1

To solve the inequality \( \frac{5x}{9} < 8 \), follow these steps:

1. Multiply both sides of the inequality by \( 9 \) to eliminate the fraction: \[ 5x < 72 \]

2. Now, divide both sides by \( 5 \): \[ x < \frac{72}{5} \]

3. Convert \( \frac{72}{5} \) into a mixed number. First, divide \( 72 \) by \( 5 \): \[ 72 \div 5 = 14 \quad \text{(with a remainder of } 2\text{)} \] So, \( \frac{72}{5} = 14 \frac{2}{5} \).

Putting it all together, the final inequality is: \[ x < 14 \frac{2}{5} \]

Thus, the answer is \( x < 14 \frac{2}{5} \).