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.

Answer 1

To solve the inequality 5x/9<8, we can begin by multiplying both sides of the inequality by 9 to get rid of the fraction:

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

This simplifies to:

5x < 72

To isolate x, we can divide both sides of the inequality by 5:

(5x)/5 < 72/5

Simplifying further:

x < 72/5

To express the improper fraction 72/5 as a mixed number, we divide the numerator (72) by the denominator (5). The quotient is the whole number part of the mixed number:

72 ÷ 5 = 14 remainder 2

Therefore, the mixed number form of 72/5 is 14 2/5.

So, the solution to the inequality 5x/9 < 8, expressed with x coming first, is:

x < 14 2/5