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To solve the inequality, we need to isolate the variable x.
The inequality is: 5x/9 < 8
To get rid of the fraction, we can multiply both sides of the inequality by 9, the denominator of the fraction.
(5x/9) * 9 < 8 * 9
This simplifies to: 5x < 72
Now, to solve for x, we divide both sides of the inequality by 5:
(5x)/5 < 72/5
This simplifies to: x < 14.4
Therefore, the solution to the inequality is x < 14.4.
Converting the improper fraction to a mixed number, we divide the numerator (8) by the denominator (9):
8 ÷ 9 = 0 remainder 8
The mixed number is 0 8/9.
So, the final answer is:
x < 0 8/9, or x < 14.4.