Absolute Value EquationsDate: 10/30/2002 at 16:53:48 From: Abel Dallas Subject: Absolute value equations What is the answer to 'the absolute value of x-3 plus the absolute value of 3-x equals 12' ? Date: 11/03/2002 at 16:56:07 From: Doctor Ian Subject: Re: Absolute value equations Hi Abel, Let's look at that: |x-3| + |x+3| = 12 The first term tells you how far x is away from 3. For example, when x is 4, |4 - 3| = |1| = 1 And when x is 2, |2 - 3| = |-1| = 1 Similarly, the second term tells you how far x is away from -3. So the in words, the equation is saying: What is x, if the distance from 3, plus the distance from -3, is 12? Let's think about how that would look on a number line. Suppose we want to test the value x = -7: |------------10---------------| x |----4------| <--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--> -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 For this value of x, the total distance is 14. Let's substitute that into the expression, and see what it says: |-7 - 3| + |-7 + 3| = |-10| + |-4| = 10 + 4 = 14 So the picture and the equation seem to be saying the same thing. The symmetry of the situation suggests that there will be two values of x such that the sum of the distances to -3 and 3 will be 12. Try to find them, and let me know what you come up with. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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