Step by step
The question
Question: if 8x + 4 = 0, what is 2x + 1?
We want 2x + 1.
Let's look for it inside the equation.
1 Compare the two
Look at 8x + 4 and 2x + 1.
We compare them part by part.
8 divided by 2 is 4.
So 8x is 4 times 2x.
4 divided by 1 is 4.
So 4 is 4 times 1.
Every part of 8x + 4 is 4 times a part of 2x + 1.
2 Take out the 4
So we can write each part as 4 times.
4 times each part is the same as 4 times the whole bracket: 4(2x + 1).
Opening the bracket gives 8x + 4 back.
3 Remove the 4
4(2x + 1) means 4 times the bracket.
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 the bracket is left.
0 divided by 4 is 0.
So 2x + 1 = 0!
Careful!
Many people find x and stop.
But the question asks for 2x + 1.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 8 and + 4.
First x was times 8.
Then + 4.
To take them off, we go backwards.
First we remove the + 4.
Then the times 8.
To remove + 4, we take away 4.
We do it on both sides, so they stay equal.
+ 4 and − 4 make zero.
Cross them out.
0 − 4 = −4.
Now we have 8x = −4.
8x means 8 times x.
We want just x.
To remove times 8, we divide by 8.
We do it on both sides, so they stay equal.
8 divided by 8 is 1.
So just x is left.
We can make −4/8 simpler.
It is the same as −1/2.
So x = −1/2!
Then 2x + 1 is 2 × (−1/2) + 1 = −1 + 1 = 0.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 4.
Then: remove the 4.
Last: check.