To solve this absolute value inequality, we need to consider two cases: when the expression inside the absolute value on the left side is positive, and when it's negative.
Case 1: When 3x + 2 is positive:
3x + 2 > x - 2
Subtract x from both sides:
2x + 2 > -2
Subtract 2 from both sides:
2x > -4
Divide by 2:
x > -2
Case 2: When 3x + 2 is negative:
-(3x + 2) > x - 2
-3x - 2 > x - 2
Subtract x from both sides:
-4x - 2 > -2
Add 2 to both sides:
-4x > 0
Divide by -4 (we also reverse the inequality when dividing by a negative number):
x < 0
Therefore, the solution to the absolute value inequality |3x+2| > |x-2| is x < 0 or x > -2.
|3x+2| > |x-2| , solve the absolute value inequality.
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