Can someone tell me how to solve this double absolute inequality?
||3-x|-2x|<=9
||3-x|-2x|<=9
Remember that if a = m, then l a l = m, if a> 0 or l a l = -m, if a < 0
Taking 3-x out of the absolute value bars, we have that either
l 3 - x - 2x l < = 9 or that l -3 + x - 2x l < = 9
And likewise, we have that
3 - x - 2x < = 9 or that 3 - x + 2x < = 9
simplify
3 - 3x < = 9 x + 3 < = 9
-3x < = 6 x < = 6
x >= -2
So -2 <= x <= 6
||3-x|-2x|<=9
Remember that if a = m, then l a l = m, if a> 0 or l a l = -m, if a < 0
Taking 3-x out of the absolute value bars, we have that either
l 3 - x - 2x l < = 9 or that l -3 + x - 2x l < = 9
And likewise, we have that
3 - x - 2x < = 9 or that 3 - x + 2x < = 9
simplify
3 - 3x < = 9 x + 3 < = 9
-3x < = 6 x < = 6
x >= -2
So -2 <= x <= 6