Question 447689: What is the solution set of |x| < 11?
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! ==> Look at the inequality sign in itself. If it is a greater-than sign, your solution set will be __ or __. If it is a less-than sign, your solution set will be __ and __. Yours is less-than, so it is an "and" problem. This will come into play later, when you state your answer.
==> Separate the inequality into two parts in order to get rid of the absolute value sign. One will be exactly the same as the original problem, but without the absolute value (x < 11). The other will be the same thing, but with the inequality sign flipped and the opposite number on the other side of the inequality sign (x > -11).
==> Normally, you would simplify these, but these are already simplified. Therefore, your answer is x < 11 and x > -11. Now is when the "and" comes in. And means the solution set must follow BOTH x < 11 AND x > -11. Or would mean that the solution set must follow EITHER ____ OR ____. You can also state and problems like -11 < x < 11; in fact, this is the way you should state them.
==> Now put into set builder notation: {x: -11 < x < 11}
***Therefore, your answer is {x: -11 < x < 11}
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