2(x - 3) = 4x + 10. What is the solution to the given equation?

Step by step

The question

Question: solve 2(x − 3) = 4x + 10.

Let's find x.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Open the brackets

The 2 in front of the bracket multiplies every part inside.

So we write 2 times each part.

Plus times minus is minus.

2 times x is 2x.

2 times (−3) is −6.

2 Get x on one side

There is x on both sides.

We want x on one side only.

The numbers in front of x are 2 and 4.

We remove the smaller one, 2x, so the x part that is left is plus.

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 cancel each other.

They make zero.

4x − 2x = 2x.

Now we have −6 = 2x + 10.

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

Both sides are the same amount, so we can swap them.

We want x by itself.

First we remove the + 10, so 2x is alone.

Then we remove the times 2.

So after step 2: we took away 2x, and now we have 2x + 10 = −6.

Is x alone now?

Not yet: + 10 is still with x.

How do we remove it?

3 Remove the + 10

To remove + 10, we take away 10.

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

+ 10 and − 10 cancel each other.

They make zero.

−6 − 10 = −16.

Now we have 2x = −16.

So after step 3: we took away 10, and now we have 2x = −16.

Is x alone now?

Not yet: 2x means 2 times x.

4 Remove the 2

To remove times 2, we divide by 2.

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

2 divided by 2 is 1.

They cancel each other.

So just x is left.

−16 divided by 2 is −8.

So x = −8!

5 Check

Let's check: put −8 in place of x.

First the left side.

Now the right side.

Both sides are −22.

So x = −8 is right!

6 Pick the choice

Our answer is x = −8.

That is choice A.

7 Why not the others

B is −13/2.

Wrong: 2x − 3 = 4x + 10: forgot 2 × 3.

C is 8/3.

Wrong: moved 4x without changing its sign: 6x = 16.

D is 8.

Wrong: lost the minus sign.

Let's look back.

First: open the brackets.

Then: get x on one side.

Then: remove the + 10.

Then: remove the 2.

Then: check.

Then: pick the choice.

Last: why not the others.