Question

Which equation is equivalent to __________

Answer 1

`(2x)/(3) - (5)/(6) = (-5x)/(12) + (1)/(4)`

<< Equate all the denominators with a ^minimum^ common number(12).


`= (4.2x)/(12) - (5.2)/(12) = (-5x)/(12) + (3)/(12)`

<< Classify same terms to one side. The fraction that you threw to other side in the equation changes.


`= (8x+5x)/(12) = (3+10)/(12)`

`(13x)/(12) (13x)/(12)`
13x=13
x=13/13
x=1

So the main equation's solution set is 1.

Let's look at the options then!

1:
`(-5)/(6) = (x)/(4) + (1)/(4)`
**equate denominators
=
`(-5)/(6) - (1)/(4) = (x)/(4)`
=
`(-10-3)/(12) = (3x)/(12)`
=
`-13=3x`
x=
`(-13)/(3)`


2:
`(2x)/(3) =(-5x)/(12) - (-7)/(12)`

`8x= -5x-7`

**throw -5x left of the equation.


`13x=-7`
x=
`(-7)/(13)`


3:
`(x)/(4) - (5)/(6) = (-1)/(4)`

`3x-10=3`
3x=7
x=7/3


4:
`(2x)/(3) - (13)/(12) = (-5x)/(12)`
8x-13= -5x
13x=13
x=1

The correct answer is 4.
Hope it helps!
#MissionExam001