Question

Please help me solve this inequality
1/3x -2 < 2/3x - 6

Answer 1

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Answer 2

1/3x - 2/3x < 2 - 6
2/3x - 1/3x > 6 - 2
1/3x > 4
x > 12

Answer 3

1/3x-2 < 2/3x -6
(1-2*3x)/3x < (2-6*3x)/3x
1-6x < 2-18x
18x-6x < 2-1
12x < 1
x < 1/12

Answer 4

x<12

Answer 5

1/3x-2 < 2/3x -6
multiply both sides by 3/2
3/2 . 1/3x -2 < 3/2 . 2/3x - 6
1/2x - 2 < x - 6
1/2x - x - 2 < -6
-1/2x -2 < -6
muliply both sides by -2
-2 . - 1/2x - 2 > -2 . -6
x - 2 > 12
x - 2 + 2 > 12 + 2
x > 14
where did I go wrong

Answer 6

the first one's supposed to be subtract both sides with 2/3x
then the second one's supposed to be add both sides by 2