Interval NotationDate: 11/01/97 at 14:34:24 From: Phil Subject: Interval notation Question: Solve for x and write the answer in interval notation: -3 < -x < 2 ___ 3 I tried to find values of x that can fit the question. Ex: making -x equal 3, dividing it by 3, and getting 1. I am reading the statement from right to left as 2 is greater than say 1 is greater than -3. I get lost when I think I am done by saying my answer is [-3] and how to show my work or even figure the question out. Can you please explain where I should start? Thank you! Phil Date: 11/01/97 at 22:18:13 From: Doctor Scott Subject: Re: Interval notation Hi Phil! Sometimes it helps to think of problems like this as being two problems connected by "and." The original statement says that -x/3 > -3 AND -x/3 < 2. These two inequalities are relatively easy to solve: just multiply both sides by 3 and divide by -1 (or multiply both sides by -3). Remember, though, that when you multiply (or divide) an inequality by a negative number, you must change the order of the inequality. So, -x/3 > -3 x < 9 <--multiply by -3 and change inequality And, -x/2 < 2 x > -4 <--multiply by -3 and change inequality So, x < 9 AND x > -4. Another way to write this is to write 9 > x > -4, which says the same thing. Or, in interval notation, (-4, 9), using parentheses because x is strictly less than 9 and strictly greater than -4, and not equal to either number. Now, with that in mind, notice that we really just did the same thing in two inequalities. So, it is sometimes convenient to combine all of the work into one step: -3 < -x/3 < 2 * -3 * -3 * -3 <--multiply all three parts by -3 to isolate the "x" in the middle. --------------------- 9 > x > -4 <--change inequality. Then, since x is between -4 and 9, we can write (-4, 9) as our solution in interval notation. -Doctor Scott, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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