solve and write in interval notation

Question

-x> 1

Answer 1

Right now, you have -x on one side of this inequality. In order to get that to equal x, you must multiply or divide both sides of the inequality by -1.

 

WARNING: When you multiply or divide both sides of an inequality by a NEGATIVE number, you MUST remember to "flip" the sign!

 

(-1)(-x) > (-1)(1)

x < -1

 

Notice how the > was flipped to a <!

 

Now, to put it in interval notation, the -1 will not be included in the interval, since < is "less than". That will give it a ), rather than a ].

 

As long as x is less than -1, the inequality will be "true" (it will "work"), so you could keep moving x down, down, down, unto negative infinity. Therefore, your interval will be:

 

(-∞, -1)

 

Positive and negative infinities are never included in intervals, so they always get a ( or ), rather than a [ or ].