Question

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

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Answer 1

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

1. Multiply both sides by 9 to eliminate the fraction:

\[
5x < 8 \times 9
\]

This simplifies to:

\[
5x < 72
\]

2. Now, divide both sides by 5:

\[
x < \frac{72}{5}
\]

3. Convert \( \frac{72}{5} \) into a mixed number. To do this, divide 72 by 5:

- 72 divided by 5 is 14 with a remainder of 2.

Thus, \( \frac{72}{5} = 14 \frac{2}{5} \).

Now, we can write the final answer with \( x \) first and the inequality:

\[
x < 14 \frac{2}{5}
\]