Step by step
The question
Question: if 3p − 2q = 5, what is 9p − 6q?
We want 9p − 6q.
Let's look for it inside the equation.
1 Compare the two
Look at 9p − 6q and 3p − 2q.
We compare them part by part.
9 divided by 3 is 3.
So 9p is 3 times 3p.
6 divided by 2 is 3.
So 6q is 3 times 2q.
Every part of 9p − 6q is 3 times a part of 3p − 2q.
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 5 is 15.
Careful!
Both sides are times 3.
5 becomes 15.
3 times 3p is 9p.
3 times −2q is −6q.
So 9p − 6q = 15!
3 Check
We can't find p and q on their own: many pairs work.
Let's check with one pair.
We pick p = 3, so that q is a small whole number.
With q = 2, 3p − 2q is 3 × 3 − 2 × 2 = 9 − 4 = 5.
It fits the question.
And 9p − 6q is 9 × 3 − 6 × 2 = 27 − 12 = 15.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 3.
Last: check.