Make x the subject of a(x - 3) = 4x + b

Step by step

The question

Question: make x the subject of a(x − 3) = 4x + 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 Open the brackets

What is in front of a bracket multiplies every part inside.

a times every part of (x − 3).

2 Get the x terms on one side

4x is on the right.

To remove it, we take away 4x.

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

Careful!

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

4x becomes −4x.

4x and −4x make zero.

Cross them out.

Now we have ax − 3a − 4x = b.

−3a has no x.

To remove it from the left, we add 3a.

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

−3a and 3a make zero.

Cross them out.

Now both x terms are on the left: ax − 4x = b + 3a.

3 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 − 4) is b + 3a.

4 Remove the (a − 4)

(a − 4)x means (a − 4) times x.

We want just x.

To remove times (a − 4), we divide by (a − 4).

We do it on both sides.

(a − 4) divided by (a − 4) is 1.

So just x is left.

So x = (b + 3a)/(a − 4).

5 Check

Let's check with numbers.

We pick a = 5, b = 2.

Our answer gives x = 17.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 17.

So our answer is right!

Let's look back.

First: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (a − 4).

Last: check.