Idon’t understand why is it “not possible”. -2/3x< 4 and 3/4x< -6 and also i don’t understand why is it “all real numbers”. 3x-9≤9 or 4-x≤3

Let's solve the inequalities: we have

and

Since the two inequality must be true at the same time (there is an "and" between the two), we should find a number that is, at the same time, greater than -6, and smaller than -8. But since -6 is greater than -8, a number greater than -6 is automatically greater than -8 as well. So, it is impossible for a number to be greater than -6 and smaller than -8.

If negative numbers confuse you, this example shows the same (impossible) logic: we can't ask for a number to be greater than 10, but smaller than 3.

As for the second exercise:

So, a number satisfies this system if it is smaller than 6 or greater than 1. This means that at least one of the conditions must be satisfied, and this is always the case:

So, whatever number we choose, at least one of the conditions will be true, and the logical "OR" will be satisfied.

sup

step-by-step explanation:

21

step-by-step explanation: