Make x the subject of ax - 5 = 2x + b

Step by step

The question

Question: make x the subject of ax − 5 = 2x + b.

The subject is the letter on its own: we want x = ...

.

Here x is in two places, so we must bring them together.

1 Get the x terms on one side

2x is on the right.

To remove it, we take away 2x.

We do it on both sides, so they stay equal.

Careful!

A term that moves to the other side changes its sign.

2x becomes −2x.

2x and −2x make zero.

Cross them out.

Now we have ax − 5 − 2x = b.

−5 has no x.

To remove it from the left, we add 5.

We do it on both sides, so they stay equal.

−5 and 5 make zero.

Cross them out.

Now both x terms are on the left: ax − 2x = b + 5.

2 Take x out

x is in every part.

So we take it out once, and write what is left in a bracket.

So x times (a − 2) is b + 5.

3 Remove the (a − 2)

(a − 2)x means (a − 2) times x.

We want just x.

To remove times (a − 2), we divide by (a − 2).

We do it on both sides.

(a − 2) divided by (a − 2) is 1.

So just x is left.

So x = (b + 5)/(a − 2).

4 Check

Let's check with numbers.

We pick a = 3, b = 2.

Our answer gives x = 7.

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: get the x terms on one side.

Then: take x out.

Then: remove the (a − 2).

Last: check.