Step by step
The question
Question: if 2x + 8 = 14, what is x + 4?
We want x + 4.
Let's look for it inside the equation.
1 Compare the two
Look at 2x + 8 and x + 4.
We compare them part by part.
2x is 2 times x.
8 divided by 4 is 2.
So 8 is 2 times 4.
Every part of 2x + 8 is 2 times a part of x + 4.
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(x + 4).
Opening the bracket gives 2x + 8 back.
3 Remove the 2
2(x + 4) 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.
14 divided by 2 is 7.
So x + 4 = 7!
Careful!
Many people find x and stop.
But the question asks for x + 4.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 2 and + 8.
First x was times 2.
Then + 8.
To take them off, we go backwards.
First we remove the + 8.
Then the times 2.
To remove + 8, we take away 8.
We do it on both sides, so they stay equal.
+ 8 and − 8 make zero.
Cross them out.
14 − 8 = 6.
Now we have 2x = 6.
2x means 2 times x.
We want just x.
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 x is left.
6 divided by 2 is 3.
So x = 3!
Then x + 4 is 3 + 4 = 7.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 2.
Then: remove the 2.
Last: check.