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