Step by step
The question
Question: if 2x + 5 = 11, what is 4x + 10?
We want 4x + 10.
Let's look for it inside the equation.
1 Compare the two
Look at 4x + 10 and 2x + 5.
We compare them part by part.
4 divided by 2 is 2.
So 4x is 2 times 2x.
10 divided by 5 is 2.
So 10 is 2 times 5.
Every part of 4x + 10 is 2 times a part of 2x + 5.
2 Multiply by 2
So we multiply both sides by 2.
We do it on both sides, so they stay equal.
Times 2 goes to every part.
2 times 11 is 22.
Careful!
Both sides are times 2.
11 becomes 22.
2 times 2x is 4x.
2 times 5 is 10.
So 4x + 10 = 22!
3 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 + 5.
First x was times 2.
Then + 5.
To take them off, we go backwards.
First we remove the + 5.
Then the times 2.
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
+ 5 and − 5 make zero.
Cross them out.
11 − 5 = 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 4x + 10 is 4 × 3 + 10 = 12 + 10 = 22.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 2.
Last: check.