Make x the subject of ax + 4 = x + b Step by Step

Step by step

The question

Question: make x the subject of ax + 4 = x + b.

ax + 4 = x + 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

x is on the right.

To remove it, we take away x.

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

ax + 4 − x = x + b ~~− x~~

Careful!

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

x becomes −x.

Careful: not ax + 4 + x = b ✗

x and −x make zero.

Cross them out.

Now we have ax + 4 − x = b.

ax + 4 − x = b

4 has no x.

To remove it from the left, we take away 4.

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

ax ~~+ 4~~ − x ~~− 4~~ = b − 4

4 and −4 make zero.

Cross them out.

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

ax − x = b − 4

2 Take x out

x is in every part.

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

ab + ac = a(b + c)

So x times (a − 1) is b − 4.

x(a − 1) = b − 4

3 Remove the (a − 1)

(a − 1)x means (a − 1) times x.

We want just x.

To remove times (a − 1), we divide by (a − 1).

We do it on both sides.

~~(a − 1)~~x~~(a − 1)~~ = b − 4(a − 1)

(a − 1) divided by (a − 1) is 1.

So just x is left.

So x = (b − 4)/(a − 1).

x = b − 4(a − 1)

4 Check

Let's check with numbers.

We pick a = 2, b = 5.

Our answer gives x = 1.

x = 5 − 42 − 1 = 11 = 1

Now we put all the numbers into the start.

First the left side.

Left: (2)(1) − 1 = 2 − 1 = 1

Now the right side.

Right: 5 − 4 = 1

Both sides are 1.

So our answer is right!

Both sides equal 1

Let's look back.

First: get the x terms on one side.

Then: take x out.

Then: remove the (a − 1).

Last: check.

Answer