Make x the subject of a(x + b) = cx Step by Step

Step by step

The question

Question: make x the subject of a(x + b) = cx.

a = cx

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 + b).

ax + ab = cx

2 Get the x terms on one side

cx is on the right.

To remove it, we take away cx.

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

ax + ab − cx = ~~cx − cx~~

Careful!

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

cx becomes −cx.

Careful: not ax + ab + cx = 0 ✗

cx and −cx make zero.

Cross them out.

Now we have ax + ab − cx = 0.

ax + ab − cx = 0

ab has no x.

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

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

ax ~~+ ab~~ − cx ~~− ab~~ = 0 − ab

ab and −ab make zero.

Cross them out.

Now both x terms are on the left: ax − cx = −ab.

ax − cx = −ab

3 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 − c) is −ab.

x(a − c) = −ab

4 Remove the (a − c)

(a − c)x means (a − c) times x.

We want just x.

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

We do it on both sides.

~~(a − c)~~x~~(a − c)~~ = −ab(a − c)

(a − c) divided by (a − c) is 1.

So just x is left.

So x = −ab over (a − c).

x = −ab(a − c)

5 Check

Let's check with numbers.

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

Our answer gives x = 3.

x = −(2)(3)2 − 4 = −6−2 = 3

Now we put all the numbers into the start.

First the left side.

Left: (2)(3) − (4)(3) = 6 − 12 = −6

Now the right side.

Right: −(2)(3) = −6

Both sides are −6.

So our answer is right!

Both sides equal −6

Let's look back.

First: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (a − c).

Last: check.

Answer