1/3x-x=-4 Need Help!?

Question

Ok, so the whole problem reads.
-1/6(x-12)+1/2(x+2)=x-1

Now heres what i`ve solved.
-1/6(x-12)+1/2(x+2)=x-1
-1/6x+2+1/2x+1=x-1
-1/6x+3/6x+1+2=x-1
2/6x+3=x-1
1/3x+3=x-1
1/3x+3-3=x-1-3
1/3x=x-4
1/3x=x-4-x

Now heres where im stuck at,
1/3x-x=-4
The way i see it is 1/3x-1(because -x = -1)
Im just not understanding how to factor in that -x with no denominator to work with, i understand the answer is -2/3x=-4 which totals out to x=6 but the part 1/3x-x=-4 has me confused.

How is -x being subtracted (added) to 1/3x as a whole number(i guess)?
I`d love a clear answer & thank you in advance.

Mark

Answer 1

1/3x=x-4 is easier to solve when written as:

x/3=x-4 which leads tp
3(x/3)=3(x-4)
x=3x-12
12=2x
6=x

Answer 2

forget about the x for the moment. What is 1/3-1? It's -2/3. Now, consider pulling the x out we have x(1/3-1)=-4 or -2/3x=-4.

Finally x=3/2*4 or 6

Answer 3

so which you're doing away with the consumer-friendly element (x+a million) and you're left with (x^2+3x-4). Then i think of you're able to understand how something is going =) =x^2(x+a million)+3x(x+a million)-4(x+a million) =(x+a million) (x^2+3x-4) =(x+a million)(x-a million)(x+4)

Answer 4

I did it this way and I don't see any problem.
-1/6(x-12)+0.5(x+2)-x+1=0
-(1/6x-2)+(0.5x+1)-x+1=0
-1/6+2+0.5x+1-x+1=0
-2/3+4=0
-2/3x=-4
2/3x=4
x=6

Answer 5

Here is how i solved it...think of it as (1/3)x-(x)=-4.
(1/3)-(1)= -2/3 x so set that equal to -4.
The negative's cancel out....giving you (2/3)x=4.
multiply each side by 3, giving you 2x=12.
Then divide by 2...giving you x=6.

Answer 6

the way i see it is thw x's cancel---- i can add or subtract them from either side of the equsion--x-x = 0--then you have1/3 of 4 =12.012012....till infinity--or 1/3x-x leaves 2/3x=4=1.4992503.....tell me if you get this right excuse my spelling