Solve y = mx + b for x

Step by step

The question

Question: solve for x in y = mx + b.

We treat the other letters like numbers.

1 x on the left

x is on the right.

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

They are still equal.

2 Remove the + b

We want x by itself.

The b is in the way.

To remove b, we take away b.

We do it on both sides.

They make zero.

Cross them out.

Now we have mx = y − b.

3 Remove the m

mx means m times x.

We want just x.

To remove times m, we divide by m.

We do it on both sides.

m divided by m is 1.

So just x is left.

So x = (y − b) over m.

4 Check

Let's check with numbers.

We pick b = 2, m = 3, y = 5.

Our answer gives x = 1.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 5.

So our answer is right!

Let's look back.

First: x on the left.

Then: remove the + b.

Then: remove the m.

Last: check.