Solve 2(x - 5) = 3(x + 1)

Step by step

The question

Question: solve 2(x − 5) = 3(x + 1).

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 left 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.

3x − 2x = x.

Now we have −10 = x + 3.

Let's swap the two sides, so x is on the left.

3 Remove the + 3

We want x by itself.

The + 3 is in the way.

To remove + 3, we take away 3.

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

+ 3 and − 3 make zero.

Cross them out.

−10 − 3 = −13.

So x = −13!

4 Check

Let's check: put −13 in place of x.

First the left side.

Now the right side.

Both sides are −36.

So x = −13 is right!

Let's look back.

First: open the brackets.

Then: get x on one side.

Then: remove the + 3.

Last: check.