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.
To solve the inequality 5x/9 < 8, we need to isolate x by multiplying both sides of the inequality by 9/5, the reciprocal of 5/9. However, when multiplying or dividing an inequality by a negative number, it is necessary to flip the inequality sign.
(5x/9) * (9/5) < 8 * (9/5)
The 9s cancel out on the left side, and on the right side, we have:
x < 72/5
To write the improper fraction 72/5 as a mixed number, we divide the numerator (72) by the denominator (5):
72 ÷ 5 = 14 with a remainder of 2
Thus, the mixed number representation of 72/5 is 14 2/5.
Therefore, the solution to the inequality 5x/9 < 8 is:
x < 14 2/5