a=3b for b

The solution for a = b=3a

did I do this backwards?

What you did makes no sense.

a=3b
divide both sides by 3
a/3=b

I still don't get it does that mean b=3

Bobpursley's answer seems easy to understand.

b = a divided by 3

I did that wrong

c=2d for d

the solution is d= c /2

Correct

if a=3b for b

The solution is b =a/3

Do I understand this correctly now?

Yes. You're right.

Yes, you did it backwards. The correct equation is a = 3b, not a = b = 3a.

To solve for b in the equation a = 3b, you need to isolate the variable b. Here's how you can do it:

1. Start with the equation: a = 3b.
2. Divide both sides of the equation by 3 to isolate the variable b. This will give you: a/3 = b.

So, the solution for b is b = a/3.

In your attempt, a = b = 3a, you are assuming that a is equal to b and 3a simultaneously, which is not correct based on the original equation a = 3b.