Solve 4(x + 1) = 2(x - 3)

Step by step

The question

Question: solve 4(x + 1) = 2(x − 3).

1 Open the brackets

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

So we write each part times what is in front.

Work out each multiplication.

2 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 2x from the right side.

To remove 2x, we take away 2x.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

2x and − 2x make zero.

Cross them out.

4x − 2x = 2x.

Now we have 2x + 4 = −6.

We want x by itself.

Two things are stuck to x: times 2 and + 4.

The + 4 is on the outside, so it comes off first.

Then the times 2.

3 Remove the + 4

To remove + 4, we take away 4.

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

+ 4 and − 4 make zero.

Cross them out.

−6 − 4 = −10.

Now we have 2x = −10.

4 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

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

2 divided by 2 is 1.

So just x is left.

−10 divided by 2 is −5.

So x = −5!

5 Check

Let's check: put −5 in place of x.

First the left side.

Now the right side.

Both sides are −16.

So x = −5 is right!

Let's look back.

First: open the brackets.

Then: get x on one side.

Then: remove the + 4.

Then: remove the 2.

Last: check.