How do you solve x/3=2/3x+1/6?

3 Answers
Apr 18, 2017

x=-1/2

Explanation:

The equation is 1/3x=2/3x+1/6

Bringing x terms to one side:

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

-1/3x=1/6

-x=3/6

x=-1/2

Apr 18, 2017

1) (1x)/3 = (2x)/3 + 1/6
2) hArr (1x)/3 - (2x)/3 - 1/6 = 0
3) hArr (2x)/6 - (4x)/6 - 1/6 = 0
4) hArr (2x - 4x -1)/6 = 0
5) hArr (-2x - 1)/6 = 0
6) rArr -2x - 1 = 0
7) hArr -2x = 1
8) hArr x = -1/2

Explanation:

1) Your equation.
2) I put everything in the same side.
3) I put everything to the same denominator.
4) I put everything on the same fraction bar.
5) I reduced the common terms.
6) « If a fraction is equal to zero, then the numerator is equal to zero. » That's a propriety.
7) I isolated the unknown value.
8) Same.

Sorry for bad English... I hope this helped you. :)

Apr 18, 2017

My first impulse would be to multiply everything by 3, just to get rid of the fractional x's.

Explanation:

->x=2x+1/2

Now subtract 2x from both sides:

->x-2x=cancel(2x)-cancel(2x)+1/2

->-x=1/2->x=-1/2