Solve 5/9x<8 . Write the improper fraction in your answer as a mixed number. Make sure to write your inequality so that x comes first.
To solve the inequality \(\frac{5}{9}x < 8\), let's start by multiplying both sides of the inequality by \(\frac{9}{5}\) to isolate \(x\).
\(\frac{5}{9}x < 8\)
\(\frac{9}{5} \cdot \frac{5}{9} x < 8 \cdot \frac{9}{5}\)
\(x < \frac{72}{5}\)
To write the improper fraction \(\frac{72}{5}\) as a mixed number, we divide the numerator (72) by the denominator (5):
Division: 72 ÷ 5 = 14 remainder 2
Therefore, the mixed number representing the improper fraction \(\frac{72}{5}\) is \(14\frac{2}{5}\).
Hence, the solution to the inequality \(\frac{5}{9}x < 8\) is \(x < 14\frac{2}{5}\).