Make x the subject of y = (3x - 2)/(x + 5)

Step by step

The question

Question: make x the subject of y = (3x − 2)/(x + 5).

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

.

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

1 Clear the fraction

The bottom, (x + 5), is in the way.

Times (x + 5) removes it.

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

(x + 5) divided by (x + 5) is 1.

Only the top is left.

Now we have y(x + 5) = 3x − 2.

2 Open the brackets

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

y times every part of (x + 5).

3 Get the x terms on one side

3x is on the right.

To remove it, we take away 3x.

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

Careful!

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

3x becomes −3x.

3x and −3x make zero.

Cross them out.

Now we have xy + 5y − 3x = −2.

5y has no x.

To remove it from the left, we take away 5y.

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

5y and −5y make zero.

Cross them out.

Now both x terms are on the left: xy − 3x = −2 − 5y.

4 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 (y − 3) is −2 − 5y.

5 Remove the (y − 3)

(y − 3)x means (y − 3) times x.

We want just x.

To remove times (y − 3), we divide by (y − 3).

We do it on both sides.

(y − 3) divided by (y − 3) is 1.

So just x is left.

So x = (−2 − 5y)/(y − 3).

6 Check

Let's check with numbers.

We pick y = 2.

Our answer gives x = 12.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are −12.

So our answer is right!

Let's look back.

First: clear the fraction.

Then: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (y − 3).

Last: check.