Solve 5x/9 < 8. Write the improper fraction in your answer as a mixed number

Answer 1

To solve the inequality 5x/9 < 8, let's first multiply both sides of the inequality by 9 to eliminate the denominator:

9*(5x/9) < 8 * 9

The 9s cancel out on the left side:

5x < 72

Next, divide both sides of the inequality by 5 to solve for x:

(5x) / 5 < 72 / 5

x < 72/5

To express the improper fraction 72/5 as a mixed number (a whole number and a proper fraction), perform the division:

72 ÷ 5 = 14 remainder 2

This implies that the quotient is 14 and the remainder is 2, so the mixed number representation of 72/5 is 14 2/5.

Therefore, the solution to the inequality 5x/9 < 8, expressed as a mixed number, is x < 14 2/5.