Step by step
The question
Question: solve 4x − 7 = 2x + 5.
1 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the right side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
4x − 2x = 2x.
Now we have 2x − 7 = 5.
We want x by itself.
Two things are stuck to x: times 2 and − 7.
The − 7 is on the outside, so it comes off first.
Then the times 2.
2 Remove the − 7
To remove − 7, we add 7.
We do it on both sides, so they stay equal.
− 7 and + 7 make zero.
Cross them out.
5 + 7 = 12.
Now we have 2x = 12.
3 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
12 divided by 2 is 6.
So x = 6!
4 Check
Let's check: put 6 in place of x.
First the left side.
Now the right side.
Both sides are 17.
So x = 6 is right!
Let's look back.
First: get x on one side.
Then: remove the − 7.
Then: remove the 2.
Last: check.