Step by step
The question
Question: solve 5 − (x + 2) = 7.
1 Open the brackets
A minus in front of a bracket changes the sign of every part inside.
x becomes −x.
2 becomes −2.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
5 − 2 = 3.
Now we have 3 − x = 7.
3 Remove the 3
We want x by itself.
The 3 is in the way.
To remove 3, we take away 3.
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.
3 and − 3 make zero.
Cross them out.
7 − 3 = 4.
Now we have −x = 4.
4 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
4 divided by −1 is −4.
So x = −4!
5 Check
Let's check: put −4 in place of x.
We get 7, the same as the right side.
So x = −4 is right!
Let's look back.
First: open the brackets.
Then: group like terms.
Then: remove the 3.
Then: remove the −1.
Last: check.