Step by step
The question
Question: solve 7 − y = 2y + 1.
1 Get y on one side
There is y on both sides.
We want y on one side only.
So we remove the −y from the left side.
To remove −y, we add y.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
− y and + y make zero.
Cross them out.
2y + y = 3y.
Now we have 7 = 3y + 1.
Let's swap the two sides, so y is on the left.
We want y by itself.
Two things are stuck to y: times 3 and + 1.
The + 1 is on the outside, so it comes off first.
Then the times 3.
2 Remove the + 1
To remove + 1, we take away 1.
We do it on both sides, so they stay equal.
+ 1 and − 1 make zero.
Cross them out.
7 − 1 = 6.
Now we have 3y = 6.
3 Remove the 3
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just y is left.
6 divided by 3 is 2.
So y = 2!
4 Check
Let's check: put 2 in place of y.
First the left side.
Now the right side.
Both sides are 5.
So y = 2 is right!
Let's look back.
First: get y on one side.
Then: remove the + 1.
Then: remove the 3.
Last: check.