Solve 5x/9 < 8

Question

. Write the improper fraction 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.

(1 point)

Answer 1

To solve the inequality \( \frac{5x}{9} < 8 \), we start by isolating \( x \).

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

\[ 5x < 8 \times 9 \]

\[ 5x < 72 \]

2. Next, divide both sides by 5 to solve for \( x \):

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

3. Now, we convert \( \frac{72}{5} \) into a mixed number. Performing the division:

\[ 72 \div 5 = 14 \quad \text{(with a remainder of } 2\text{)} \]

So:

\[ \frac{72}{5} = 14 \frac{2}{5} \]

4. Therefore, the final inequality is:

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

So the answer is: \[ x < 14 \frac{2}{5} \]