Step by step
The question
Question: solve 6n − 4 = 2n − 4.
1 Get n on one side
There is n on both sides.
We want n on one side only.
So we remove the 2n from the right side.
To remove 2n, we take away 2n.
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.
2n and − 2n make zero.
Cross them out.
6n − 2n = 4n.
Now we have 4n − 4 = −4.
We want n by itself.
Two things are stuck to n: times 4 and − 4.
The − 4 is on the outside, so it comes off first.
Then the times 4.
2 Remove the − 4
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
−4 + 4 = 0.
Now we have 4n = 0.
3 Remove the 4
4n means 4 times n.
We want just n.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just n is left.
0 divided by 4 is 0.
So n = 0!
4 Check
Let's check: put 0 in place of n.
First the left side.
Now the right side.
Both sides are −4.
So n = 0 is right!
Let's look back.
First: get n on one side.
Then: remove the − 4.
Then: remove the 4.
Last: check.