Step by step
The question
Question: solve 5(x − 2) = 3x + 6.
Let's find x.
1 Open the brackets
The 5 in front of the bracket multiplies every part inside.
So we write 5 times each part.
Plus times minus is minus.
5 times x is 5x.
5 times (−2) is −10.
2 Get x on one side
There is x on both sides.
We want x on one side only.
The numbers in front of x are 3 and 5.
We remove the smaller one, 3x, so the x part that is left is plus.
So we remove the 3x from the right side.
To remove 3x, we take away 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 cancel each other.
They make zero.
5x − 3x = 2x.
Now we have 2x − 10 = 6.
We want x by itself.
First we remove the − 10, so 2x is alone.
Then we remove the times 2.
So after step 2: we took away 3x, and now we have 2x − 10 = 6.
Is x alone now?
Not yet: − 10 is still with x.
How do we remove it?
3 Remove the − 10
To remove − 10, we add 10.
We do it on both sides, so they stay equal.
− 10 and + 10 cancel each other.
They make zero.
6 + 10 = 16.
Now we have 2x = 16.
So after step 3: we added 10, and now we have 2x = 16.
Is x alone now?
Not yet: 2x means 2 times x.
4 Remove the 2
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
They cancel each other.
So just x is left.
16 divided by 2 is 8.
So x = 8!
5 Check
Let's check: put 8 in place of x.
First the left side.
Now the right side.
Both sides are 30.
So x = 8 is right!
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: remove the − 10.
Then: remove the 2.
Last: check.