Solve for x

Hi, Devyn.

I read the question as:

1/4 x + x = 3 + 1/2 x

So here is how to work this equation. You can combine the terms on the left hand side, 1/4 x + x

Remember that a plain x is the same as 1x, so adding them together gives you 1 1/4 x. (That is supposed to be a mixed number, a whole number 1 and the fraction 1/4.)

You can leave that in the improper form, 5/4 x to make the subtraction easier in the next step.

so you now have: 5/4 x = 3 + 1/2 x

You have to subtract the 1/2 x from both sides to get all the variables on one side of the equation. To subtract fractions you have to have the same denominator, so we will rewrite 1/2 x as 2/4 x

5/4 x - 2/4 x = 3 + 2/4 x - 2/4 x

The + 2/4 x - 2/4 x cancels out, so you have:

3/4 x = 3

To undo the 3/4 times x, you would divide by 3/4. BUT, remember that when you divide by a fraction, you actually multiply the reciprocal (turn the fraction over). So: (the asterisk stands for multiplication)

3/4 x * 4/3 = 3 * 4/3

The 3/4 and 4/3 cancel out; on the right you multiply 3/1 by 4/3

x = 12/3 which simplifies to x = 4

You can check it by substituting 4 back into the original equation:

1/4 * 4 + 4 = 3 + 1/2 * 4

That simplifies to 1 + 4 = 3 + 2 which is true, so our solution works.

## Comments

Is it (1/4)x or (1/4x)?