Need help solving equation involving fractions

[CMUChippewa1]

I need help in solving the following equation:

1/4 (8x-12)=6 (1/3x-1/2)+10 (the x is next to the 1/3, not next to the 3 in the problem)

Every time I try to solve it I end up with 0x=10, which I know is incorrect. Any help that I can receive would be appreciated!

 

[stapel]

Every time I try to solve it....

We'll be glad to help you find your error. But you'll need to post all your steps, in order for us to do so.

Thank you.

Eliz.

 

[CMUChippewa1]

Steps I took to try to solve the equation involving fraction

Problem: 1/4 (8x-12)=6 (1/3x-1/2) + 10 ( the x is next to the 1/3, not next to the 3)

First, I multiplied the expressions in the parentheses.

8x/4-12/4= 6/3x - 1/2 + 10

2x-3 = 2x -3 + 10

Then, I combined like terms.

2x -3 =2x+ 7

This is where I am confused because the 2xs will cancel each other out.

Thanks in advance for your assistance.

 

[stapel]

When the variables cancel out, there are two solution options:

i) the variable doesn't matter, because the equation is always true

ii) the equation is nonsense, and there is no solution

An example of (i) would be "x + 1 = (1/2)(2x + 2)". The value of "x" is irrelevant; the equation is always true.

An example of (ii) would be "x - 1 = x + 1". The value of "x" is again irrelevant, but this time it's because no value could possibly solve this equation. The equation itself is nonsense, since (subtracting "x" from either side) -1 will never equal +1.

The "answer" for (i) is "all x" or "all reals"; the "answer" for (ii) is "no solution".

Eliz.

Note: Duplicate posting of this exercise has been deleted.