Step by step
The question
Question: solve 4(2x − 3) = 5(x + 6).
Let's find x.
1 Open the brackets
What is in front of a bracket multiplies every part inside.
So we write each part times what is in front.
Plus times minus is minus.
4 times 2x is 8x.
4 times (−3) is −12.
5 times x is 5x.
5 times 6 is 30.
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 5 and 8.
We remove the smaller one, 5x, so the x part that is left is plus.
So we remove the 5x from the right side.
To remove 5x, we take away 5x.
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.
5x and − 5x cancel each other.
They make zero.
8x − 5x = 3x.
Now we have 3x − 12 = 30.
We want x by itself.
First we remove the − 12, so 3x is alone.
Then we remove the times 3.
So after step 2: we took away 5x, and now we have 3x − 12 = 30.
Is x alone now?
Not yet: − 12 is still with x.
How do we remove it?
3 Remove the − 12
To remove − 12, we add 12.
We do it on both sides, so they stay equal.
− 12 and + 12 cancel each other.
They make zero.
30 + 12 = 42.
Now we have 3x = 42.
So after step 3: we added 12, and now we have 3x = 42.
Is x alone now?
Not yet: 3x means 3 times x.
4 Remove the 3
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
They cancel each other.
So just x is left.
42 divided by 3 is 14.
So x = 14!
5 Check
Let's check: put 14 in place of x.
First the left side.
Now the right side.
Both sides are 100.
So x = 14 is right!
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: remove the − 12.
Then: remove the 3.
Last: check.