Step by step
The question
Question: if 4x + 6 = 9, what is 2x + 3?
We want 2x + 3.
Let's look for it inside the equation.
1 Compare the two
Look at 4x + 6 and 2x + 3.
We compare them part by part.
4 divided by 2 is 2.
So 4x is 2 times 2x.
6 divided by 3 is 2.
So 6 is 2 times 3.
Every part of 4x + 6 is 2 times a part of 2x + 3.
2 Take out the 2
So we can write each part as 2 times.
2 times each part is the same as 2 times the whole bracket: 2(2x + 3).
Opening the bracket gives 4x + 6 back.
3 Remove the 2
2(2x + 3) means 2 times the bracket.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just the bracket is left.
9/2 can't be made simpler.
So it stays a fraction.
So 2x + 3 = 9/2!
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 4 and + 6.
First x was times 4.
Then + 6.
To take them off, we go backwards.
First we remove the + 6.
Then the times 4.
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
+ 6 and − 6 make zero.
Cross them out.
9 − 6 = 3.
Now we have 4x = 3.
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.
So x = 3/4!
Then 2x + 3 is 2 × 3/4 + 3 = 3/2 + 3 = 9/2.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 2.
Then: remove the 2.
Last: check.