Question

solve 5x/9<8 write as an improper fraction

Answer 1

To solve the inequality 5x/9 < 8, we can start by multiplying both sides of the inequality by 9 to eliminate the fraction. However, when we multiply by a negative number, the direction of the inequality must be flipped. Thus, we need to consider two cases:

Case 1: When 9 is positive
(9)(5x/9) < (9)(8)
5x < 72

Case 2: When 9 is negative
(9)(5x/9) > (9)(8)
5x > 72

Now, let's solve each case separately:

Case 1:
5x < 72
We can solve this inequality by dividing both sides by 5:
5x/5 < 72/5
x < 14 2/5

Case 2:
5x > 72
Again, divide both sides by 5:
5x/5 > 72/5
x > 14 2/5

Therefore, the solution to the inequality 5x/9 < 8 as an improper fraction is:
x < 14 2/5 or x > 14 2/5