Step by step
The question
Question: if x + 3 = 10, what is 2x + 6?
We want 2x + 6.
Let's look for it inside the equation.
1 Compare the two
Look at 2x + 6 and x + 3.
We compare them part by part.
2x is 2 times x.
6 divided by 3 is 2.
So 6 is 2 times 3.
Every part of 2x + 6 is 2 times a part of x + 3.
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 10 is 20.
Careful!
Both sides are times 2.
10 becomes 20.
2 times x is 2x.
2 times 3 is 6.
So 2x + 6 = 20!
3 Check
Let's check the long way: first we find x.
We want x by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
10 − 3 = 7.
So x = 7!
Then 2x + 6 is 2 × 7 + 6 = 14 + 6 = 20.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 2.
Last: check.