Left side = right side check type of question.

x - (x + y)/2 = (x - y)/2

What I did was times the x in the left side by 2. I got:
=(2x-x+y)/2
which equals
=(x+y)/2

But the left side is (x-y)/2. What am I doing wrong?

time x in the left side by 2?

then (2x-x-y)/2= (x-y)/2

but the left side has a negative sign in between the x and y, and if you multiply it by -2, it makes the x negative.

In order to understand what went wrong, let's go step by step and analyze your solution.

You began by multiplying the x on the left side of the equation by 2, which is a good first step. This gives you:

2 * x - (x + y)/2 = (x - y)/2

The next step you took was to distribute the 2 to both terms inside the parentheses on the left side:

2x - (x + y)/2 = (x - y)/2

This step is correct. However, when you simplified the expression, you made a mistake. You wrote:

= (2x - x + y)/2

This is where the error occurred. Let's examine the mistake further:

In the numerator, you subtracted x from 2x, which is correct. However, you incorrectly added y to the numerator instead of subtracting it. This mistake causes the incorrect simplification:

=(2x-x+y)/2

To correct this error, you need to subtract y from the numerator:

=(2x-x-y)/2

Now, let's continue simplifying the expression:

=(x-y)/2

After correcting the mistake, we obtain (x-y)/2, which matches the left side of the original equation. Therefore, the corrected solution is:

2 * x - (x + y)/2 = (x - y)/2
=(x - y)/2

So, the left side is indeed equal to the right side, and you have found the correct solution. The error in your initial simplification occurred when you mistakenly added y instead of subtracting it.