Homework Help Forum: trig

Posted by Andy on Wednesday, October 28, 2009 at 8:39pm.

lx - 2l - lx + 2l > x The absolute value of x - 2 minus the absolute value of x + 2 greater than x. What is the Answer Please Help!

• trig - Reiny, Wednesday, October 28, 2009 at 9:51pm

  x-2 > x + │x+2│ OR -x+2 > x + │x+2│ -2 > │x+2│ or -2x + 2 > │x+2│ -2 > │x+2│ is the same as │x+2│ < -2 which is not true by definition of absolute value. So -2x + 2 > │x+2│ then │x+2│ < -2x + 2 then x+2 < -2x+2 AND -x-2 < -2x + 2 3x < 0 AND x < 4 so x < 0

  
  

• trig - jim, Wednesday, October 28, 2009 at 10:08pm

  Ask yourself this: 1. If x>0, is |x - 2| - |x + 2| positive or negative or zero? (or think of it as "is |x - 2| > |x + 2| ?" 2. If x==0, then clearly |x - 2| - |x + 2| is zero. 3. Now, the interesting one: what if x is negative? Then is |x - 2| > |x + 2| ?

  
  

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