Solve T = 2a + 3b for b

Step by step

The question

Question: solve for b in T = 2a + 3b.

We treat the other letters like numbers.

1 b on the left

b is on the right.

We swap the two sides, so b is on the left.

They are still equal.

2 Remove the 2a

We want b by itself.

The 2a is in the way.

To remove 2a, we take away 2a.

We do it on both sides.

They make zero.

Cross them out.

Now we have 3b = T − 2a.

3 Remove the 3

3b means 3 times b.

We want just b.

To remove times 3, we divide by 3.

We do it on both sides.

3 divided by 3 is 1.

So just b is left.

So b = (T − 2a)/3.

4 Check

Let's check with numbers.

We pick T = 7, a = 2.

Our answer gives b = 1.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 7.

So our answer is right!

Let's look back.

First: b on the left.

Then: remove the 2a.

Then: remove the 3.

Last: check.