Make x the subject of m(x + 2) = n(x

Step by step

The question

Question: make x the subject of m(x + 2) = n(x − 5).

m = n

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.

m times every part of (x + 2).

n times every part of (x − 5).

mx + 2m = nx − 5n

2 Get the x terms on one side

nx is on the right.

To remove it, we take away nx.

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

mx + 2m − nx = nx − 5n ~~− nx~~

Careful!

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

nx becomes −nx.

Careful: not mx + 2m + nx = −5n ✗

nx and −nx make zero.

Cross them out.

Now we have mx + 2m − nx = −5n.

mx + 2m − nx = −5n

2m has no x.

To remove it from the left, we take away 2m.

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

mx ~~+ 2m~~ − nx ~~− 2m~~ = −5n − 2m

2m and −2m make zero.

Cross them out.

Now both x terms are on the left: mx − nx = −5n − 2m.

mx − nx = −5n − 2m

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 (m − n) is −5n − 2m.

x(m − n) = −5n − 2m

4 Remove the (m − n)

(m − n)x means (m − n) times x.

We want just x.

To remove times (m − n), we divide by (m − n).

We do it on both sides.

~~(m − n)~~x~~(m − n)~~ = −5n − 2m(m − n)

(m − n) divided by (m − n) is 1.

So just x is left.

So x = (−5n − 2m)/(m − n).

x = −5n − 2m(m − n)

5 Check

Let's check with numbers.

We pick m = 2, n = 3.

Our answer gives x = 19.

x = −5(3) − 2(2)2 − 3 = −15 − 4−1 = −19−1 = 19

Now we put all the numbers into the start.

First the left side.

Left: (2)(19) − (3)(19) = 38 − 57 = −19

Now the right side.

Right: −5(3) − 2(2) = −15 − 4 = −19

Both sides are −19.

So our answer is right!

Both sides equal −19

Let's look back.

First: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (m − n).

Last: check.

Answer