Step by step
The question
Question: solve 5 − 3x = x + 13.
1 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the −3x from the left side.
To remove −3x, we add 3x.
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.
− 3x and + 3x make zero.
Cross them out.
x + 3x = 4x.
Now we have 5 = 4x + 13.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 4 and + 13.
The + 13 is on the outside, so it comes off first.
Then the times 4.
2 Remove the + 13
To remove + 13, we take away 13.
We do it on both sides, so they stay equal.
+ 13 and − 13 make zero.
Cross them out.
5 − 13 = −8.
Now we have 4x = −8.
3 Remove the 4
4x means 4 times x.
We want just x.
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 x is left.
−8 divided by 4 is −2.
So x = −2!
4 Check
Let's check: put −2 in place of x.
First the left side.
Now the right side.
Both sides are 11.
So x = −2 is right!
Let's look back.
First: get x on one side.
Then: remove the + 13.
Then: remove the 4.
Last: check.