Ax - b = c for x

Step by step

The question

Question: solve for x in ax − b = c.

We treat the other letters like numbers.

1 Remove the − b

We want x by itself.

The −b is in the way.

To remove −b, we add b.

We do it on both sides.

They make zero.

Cross them out.

Now we have ax = c + b.

2 Remove the a

ax means a times x.

We want just x.

To remove times a, we divide by a.

We do it on both sides.

a divided by a is 1.

So just x is left.

So x = (c + b) over a.

3 Check

Let's check with numbers.

We pick a = 3, b = 2, c = 4.

Our answer gives x = 2.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 4.

So our answer is right!

Let's look back.

First: remove the − b.

Then: remove the a.

Last: check.