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
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!
2 answers
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| ?
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| ?