Solving Absolute Value FunctionsDate: 07/19/98 at 23:56:11 From: Rich Subject: Absolute Value Problems How do you solve |4/7x + 6| + 3 = 15? Date: 07/21/98 at 15:57:25 From: Doctor Margaret Subject: Re: Absolute Value Problems Hi Rich, Thanks for writing to us. This equation actually has to be solved twice because of the absolute value. The absolute value of a number is its distance from zero on the number line. Distance is always a positive number or zero, so the absolute value of a number is always a positive number or zero. The distance from 0 to 3 on the number line is three units and the distance from -3 to 0 is also three units. Thus: |3| = 3 and |-3| = 3 To solve an equation containing an absolute value sign, remove the sign and rewrite it as two equations. For example: |x + 2| = 8 turns out to be: x + 2 = 8 and -(x + 2) = 8 x = 6 -x - 2 = 8 <-- distribute the negative -x = 10 on the entire x = -10 expression So the answers are 6 and -10. Plugging them back into the equation: |6 + 2| = 8 and |-10 + 2| = 8 |8| = 8 |-8| = 8 These two answers are correct. Now it's your turn to try. Let me know how you did, or if you need more help. - Doctor Margaret, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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