Make x the subject of 2(x + a) = b(x

Step by step

The question

Question: make x the subject of 2(x + a) = b(x − 1).

2 = 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.

2 times every part of (x + a).

b times every part of (x − 1).

2x + 2a = bx − b

2 Get the x terms on one side

bx is on the right.

To remove it, we take away bx.

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

2x + 2a − bx = bx − b ~~− bx~~

Careful!

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

bx becomes −bx.

Careful: not 2x + 2a + bx = −b ✗

bx and −bx make zero.

Cross them out.

Now we have 2x + 2a − bx = −b.

2x + 2a − bx = −b

2a has no x.

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

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

2x ~~+ 2a~~ − bx ~~− 2a~~ = −b − 2a

2a and −2a make zero.

Cross them out.

Now both x terms are on the left: 2x − bx = −b − 2a.

2x − bx = −b − 2a

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 (2 − b) is −b − 2a.

x(2 − b) = −b − 2a

4 Remove the (2 − b)

(2 − b)x means (2 − b) times x.

We want just x.

To remove times (2 − b), we divide by (2 − b).

We do it on both sides.

~~(2 − b)~~x~~(2 − b)~~ = −b − 2a(2 − b)

(2 − b) divided by (2 − b) is 1.

So just x is left.

So x = (−b − 2a)/(2 − b).

x = −b − 2a(2 − b)

5 Check

Let's check with numbers.

We pick a = 2, b = 3.

Our answer gives x = 7.

x = −3 − 2(2)2 − 3 = −3 − 4−1 = −7−1 = 7

Now we put all the numbers into the start.

First the left side.

Left: 2(7) − (3)(7) = 14 − 21 = −7

Now the right side.

Right: −3 − 2(2) = −3 − 4 = −7

Both sides are −7.

So our answer is right!

Both sides equal −7

Let's look back.

First: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (2 − b).

Last: check.

Answer