can someone please correct my mistakes?

Question

x/2-(3x-1)/3 < 1/4
i did: x/2 times 2 - (3x-1)/3 < 1/4 times 2 (then i crossed out)
becomes:
x-(3x-1)/3 times 3 < 1/2 times 3 (crossed them out)
= x-3x+1 < 3/2 => -2x +1 <3/2 -1 => -2x<3/2-( 1/1) times 2 both deno and numerator
= -2x/-2 < 3/2-1 = x > -0.25

Answer 1

x / 2 - ( 3 x - 1 ) / 3 = [ 3 x - 2 ( 3 x - 1 ) ] / 6 = ( 3 x - 6 x + 2 ) / 6 = ( - 3 x + 2 ) / 6

x / 2 - ( 3 x - 1 ) / 3 < 1 / 4

( - 3 x + 2 ) / 6 < 1 / 4 Multiply both sides by 6

- 3 x + 2 < 6 / 4 Multiply both sides by 4

- 12 x + 8 < 6 Subtract 8 to both sides

- 12 x + 8 - 8 < 6 - 8

- 12 x < - 2 Divide both sides by - 12

________________________________________

Remark :

When you multiply or divide left and right sides of inequality , you must change the direction of the inequality.

________________________________________

- 12 x / - 12 > - 2 / - 12

x > - 2 / - ( 2 * 6 )

x > 1 / 6

Answer 2

When you multiply or divide left and right sides of inequality WITH NEGATIVE NUMBER , you MUST CHANGE the direction of the inequality

Answer 3

you forgot to multiply the second term
-(3x-1)/3 by 2 in your first multiplication and then
again you forgot to multiply the first term x by 3 in your second round

I would have multiplied each side by 12 , the LCD

6x - 4(3x-1) < 3
6x - 12x + 4 < 3
-6x < -1
x > 1/6

Answer 4

Nooo im so sorry i meant its x/2 -(3x+1)/3. < 1/4

Answer 5

same steps, you would still have your same errors!

x/2 -(3x+1)/3. < 1/4
times 12
6x - 4(3x+1) < 3
6x - 12x - 4 ≤ 3
-6x ≤ 7
x ≥ -7/6

Did you not read the part where I told you what your error was ???

Answer 6

I did, i know my mistakes now :) thanks

Answer 7

But why did you multiply both my 12 instead of 6

Answer 8

I see denominators of
2 , 3, and 4

and for those the LCD is 12 , not 6