Question

2/3x-1/2=x+7/6

How do I do this?
Please give step by step

Answer 1

--------------------------------------------------------------------------------
Question
--------------------------------------------------------------------------------

`(2)/(3)x - (1)/(2) = x + (7)/(6)`

--------------------------------------------------------------------------------
Rewrite the right to the left
--------------------------------------------------------------------------------

`x + (7)/(6) = (2)/(3)x - (1)/(2)`

--------------------------------------------------------------------------------
Take away 2/3x from both sides
--------------------------------------------------------------------------------

`x + (7)/(6) - (2)/(3)x= (2)/(3)x - (1)/(2) - (2)/(3)x`

`x - (2)/(3)x + (7)/(6)= (2)/(3)x - (2)/(3)x - (1)/(2)`

`(7)/(6) + (1)/(3)x= - (1)/(2)`

--------------------------------------------------------------------------------
Take away 7/6 from both sides
--------------------------------------------------------------------------------

`(7)/(6) + (1)/(3)x - (7)/(6) = - (1)/(2) - (7)/(6)`

`(7)/(6) - (7)/(6) + (1)/(3)x = - (1)/(2) - (7)/(6)`

`(1)/(3)x = - (1)/(2) - (7)/(6)`

--------------------------------------------------------------------------------
Change the denominator to be the same and minus
--------------------------------------------------------------------------------

`(1)/(3)x = - (3)/(6) - (7)/(6)`

`(1)/(3)x = - (10)/(6)`

--------------------------------------------------------------------------------
Multiply by 6 on both sides
--------------------------------------------------------------------------------

`2x= -10`

--------------------------------------------------------------------------------
Divide by 2 both sides
--------------------------------------------------------------------------------

`x = -5`

--------------------------------------------------------------------------------
Answer : x = -5
--------------------------------------------------------------------------------