Question

How do you solve `5- \frac { x } { 3} = x - \frac { 1} { 3}`?

Answer 1

By arranging equation `x=4`

Explanation:

Let me collect numbers on left hand side and xs on right hand side:

`5+1/3 = x+x/3`

`16/3 = 4x/3`

`16=(3*4x)/3`

`16=4x`

and

`x=4`

Your answer is `x=4`.

Answer 2

`x=4`

Explanation:

`"to eliminate the fractions, multiply ALL terms by 3"`

`(3xx5)-(cancel(3)xxx/cancel(3))=(3xxx)-(cancel(3)xx1/cancel(3))`

`rArr15-x=3x-1larrcolor(red)" no fractions"`

`"add x to both sides"`

`15cancel(-x)cancel(+x)=3x+x-1`

`rArr15=4x-1`

`"add 1 to both sides"`

`15+1=4xcancel(-1)cancel(+1)`

`rArr4x=16larr" reversing equation"`

`"divide both sides by 4"`

`rArrx=4`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides equate then it is the solution.

`"left side "=5-4/3=15/3-4/3=11/3`

`"right side "=4-1/3=12/3-1/3=11/3`

`rArrx=4" is the solution"`