Step by step
The question
Question: if 2a − b = 7, what is 6a − 3b?
We want 6a − 3b.
Let's look for it inside the equation.
1 Compare the two
Look at 6a − 3b and 2a − b.
We compare them part by part.
6 divided by 2 is 3.
So 6a is 3 times 2a.
3b is 3 times b.
Every part of 6a − 3b is 3 times a part of 2a − b.
2 Multiply by 3
So we multiply both sides by 3.
We do it on both sides, so they stay equal.
Times 3 goes to every part.
3 times 7 is 21.
Careful!
Both sides are times 3.
7 becomes 21.
3 times 2a is 6a.
3 times −b is −3b.
So 6a − 3b = 21!
3 Check
We can't find a and b on their own: many pairs work.
Let's check with one pair.
We pick a = 4, so that b is a small whole number.
With b = 1, 2a − b is 2 × 4 − 1 = 8 − 1 = 7.
It fits the question.
And 6a − 3b is 6 × 4 − 3 × 1 = 24 − 3 = 21.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 3.
Last: check.