Question

What are the solutions of the inequality?

x/9 > 9

x/5 >= -2

-x/4 <= 2

-4x >= -12

Answer 1

You want to solve them similarly to any other equation but remember that when you divide a negative number the inequality sign reverses. so the first one is \[9*(x/9)>9*9 \rightarrow x>81\] Another example is \[(-1/4)*(-4x)>=(-12)*(-1/4)\rightarrow x<=3\]

Answer 2

Notice on the second problem that the inequality sign has reversed due to the division by a negative number.