Step by step
The question
Question: if a + b = 6, what is 4a + 4b?
We want 4a + 4b.
Let's look for it inside the equation.
1 Compare the two
Look at 4a + 4b and a + b.
We compare them part by part.
4a is 4 times a.
4b is 4 times b.
Every part of 4a + 4b is 4 times a part of a + b.
2 Multiply by 4
So we multiply both sides by 4.
We do it on both sides, so they stay equal.
Times 4 goes to every part.
4 times 6 is 24.
Careful!
Both sides are times 4.
6 becomes 24.
4 times a is 4a.
4 times b is 4b.
So 4a + 4b = 24!
3 Check
We can't find a and b on their own: many pairs work.
Let's check with one pair.
We pick a = 1, so that b is a small whole number.
With b = 5, a + b is 1 + 5 = 6.
It fits the question.
And 4a + 4b is 4 × 1 + 4 × 5 = 4 + 20 = 24.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 4.
Last: check.