Solving Inequalities by Reasoning
Date: 9/8/95 at 11:18:47 From: Anonymous Subject: Algebra 2 Honors This is my first day in Algebra 2 Honors at Harbor High School in Santa Cruz,California. I am in the 10th grade. Can you help me with this problem? "1 is less than or equal to (4 - 5K) is less than 9" Thanks very much for your help. Annie
Date: 9/13/95 at 15:42:45 From: Doctor Steve Subject: Re: Algebra 2 Honors Hi Annie, You can do similar sorts of operations to inequalities as you can to equations. For instance you can add or multiply a number to all parts of the inequality. You just have to be careful about how it affects the inequality. For instance, suppose we had 1 ≤ x ≤ 8. If we multiply all the parts by -1, what happens? You can figure this out just by thinking for a bit. If x is between 1 and 8 then -x is between -1 and -8. But -8 is smaller than -1 so something will have to change in the way the inequality is written besides just adding negative signs if it's to make sense. If we don't change anything else we would get nonsense: -1 ≤ -x ≤-8. How could it be both bigger than -1 AND smaller than -8? So the correct way to write the result of multiplying by -1 would be: -1 ≥ -x ≥ -8 So, back to your problem. We can estimate by looking at approximately what K is, right? This is always good to do so that your common sense can check your calculations. K can't be as big as 1 and it can't be smaller than -1. Do you see why I say that? So now you can start trying to isolate K. I would first subtract 4 from each part and then divide by -5. This would be easier if the inequality began with -1 instead of 1. Did you make a typo there? Let me know if you can't finish this. - Doctor Steve, The Geometry Forum
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