Step by step
The question
Question: if 6x + 9 = 33, what is 2x + 3?
We want 2x + 3.
Let's look for it inside the equation.
1 Compare the two
Look at 6x + 9 and 2x + 3.
We compare them part by part.
6 divided by 2 is 3.
So 6x is 3 times 2x.
9 divided by 3 is 3.
So 9 is 3 times 3.
Every part of 6x + 9 is 3 times a part of 2x + 3.
2 Take out the 3
So we can write each part as 3 times.
3 times each part is the same as 3 times the whole bracket: 3(2x + 3).
Opening the bracket gives 6x + 9 back.
3 Remove the 3
3(2x + 3) means 3 times the bracket.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just the bracket is left.
33 divided by 3 is 11.
So 2x + 3 = 11!
Careful!
Many people find x and stop.
But the question asks for 2x + 3.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 6 and + 9.
First x was times 6.
Then + 9.
To take them off, we go backwards.
First we remove the + 9.
Then the times 6.
To remove + 9, we take away 9.
We do it on both sides, so they stay equal.
+ 9 and − 9 make zero.
Cross them out.
33 − 9 = 24.
Now we have 6x = 24.
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
So just x is left.
24 divided by 6 is 4.
So x = 4!
Then 2x + 3 is 2 × 4 + 3 = 8 + 3 = 11.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Last: check.