You have to keep in mind that you can get 2 different outcomes.
For example, we can take the absolute inequality:
l4x-12l > 8
In order to get both possible solutions, you need to write two different equations without the absolute value symbols.
One would be as written:
And you can simplify this down:
For the second outcome, you have to take into account the negative values that could come out of an absolute value equation. Because absolute value is the distance of units away from 0, negative matters.
In order to do this, we can create another equation where we switch the sign around and make one side negative, again taking away the absolute value symbols.
4x-12<-8 or -(4x-12)>8
I would recommend using the first one though because sometimes people forget to distribute the negative in the second equation. Either way, it simplifies down to:
To make sure this is correct, we can check each equation using a number that complies with the rule with our original equation. For example, if x>5, we should use a number that's greater than 5 and not 5 or else the outcome will equal 8. So in this case, we'll use 6.
l4(6)-12l > 8
If we used 4, the answer would turn out to be 4>8 which isn't right.
Therefore, our answer from before is correct.
Same goes for the other outcome, we can use a number less than 1, so we'll use 0.
l4(0)-12l > 8
l0-12l > 8
l-12l > 8
If we used 2, the answer would turn out to be 4>8 which isn't right. Therefore, our answer from before is correct.