# Thread: flipping the inequality sign

1. ## flipping the inequality sign

When working with inequalities, what are the rules for flipping the ineqaulity sign around when you move the variable around. I know when dividing by a negative we flip. Do we flip the sign around so that it is always oriented with the same orientation it began as. Since the variable could be neg or positive do we wind up with two possible answers depending on the sign if we divide by the variable.

2. if you divide both sides by a negative number, flip the sign.

if you multiply both sides by a negative number, flip the sign.

the sign may have either orientation, inequalities are better or worse by being greater than instead of less than.

3. ## variable?

yes i know the rule for negative number operations. i am asking what is the rule when we work with the variable.

4. Originally Posted by manyarrows
yes i know the rule for negative number operations. i am asking what is the rule when we work with the variable.
If the variable can be either positive or negative (or zero), you will need to consider each case separately.

However, if you know that the quantity you are multiplying or dividing by is positive (or if you know that it is negative), then you can follow the standard procedure. For example, when multiplying by $-(x^2+1),$ which is negative regardless of the value of $x$, you must flip the sign.