Interpreting "Less" and "Less Than" in Word Problems
Date: 10/18/2004 at 20:49:37 From: Charles Subject: A tough word problem that I cannot crack. Find all numbers such that 9 less than the product of the number and -4 is less than 7. The confusion comes when the sentence breaks into two parts, like this: 9 < x = -4 < 7
Date: 10/18/2004 at 22:22:38 From: Doctor Peterson Subject: Re: A tough word problem that I cannot crack. Hi, Charles. The words "greater" and "less" in a problem are often tricky, because they can be used in different ways: 5 is less than x means 5 < x 5 less than x means x - 5 5 less x means 5 - x Your problem uses the first two! You aren't told that "9 IS less than ...", but that "9 less than [something] IS less than 7". Here is how I think through a sentence like yours: "9 less than ..." We're going to be subtracting 9 from something; what is it? "... the product of the number and -4 ..." There are two numbers being multiplied, namely x and -4. That's what we have to start with: (x)(-4), from which we subtract 9. So we have -4x - 9 "... is less than 7" The expression we've just found is less than 7, so we have the inequality -4x - 9 < 7 Now you can solve it. If you need more help, please write back and show me how far you got. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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