Question

please help me clarify where did I go wrong with solving this inequality 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?

Answer 1

when u multiplied the inequality by '2', u forgot to multiply it with the already present digit '2'

Answer 2

-2(-1/2x-2) > -2.-6
x+4 > 12
x > 8

Answer 3

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