If 6(x - 2) = 4x + 10, what is the value of x? Step by Step

Step by step

The question

Question: solve 6(x − 2) = 4x + 10.

6(x − 2) = 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 6 in front of the bracket multiplies every part inside.

So we write 6 times each part.

6 × x + 6 × (−2) = 4x + 10

Plus times minus is minus.

+ × − = −

6 times x is 6x.

6 times (−2) is −12.

6x − 12 = 4x + 10

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 4 and 6.

We remove the smaller one, 4x, so the x part that is left is plus.

So we remove the 4x from the right side.

To remove 4x, we take away 4x.

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.

6x − 12 − 4x = 4x + 10 ~~− 4x~~

4x and − 4x cancel each other.

They make zero.

6x − 4x = 2x.

6x − 4x = 2x

Now we have 2x − 12 = 10.

2x − 12 = 10

We want x by itself.

First we remove the − 12, so 2x is alone.

Then we remove the times 2.

So after step 2: we took away 4x, and now we have 2x − 12 = 10.

← step 2: took away 4x

Is x alone now?

Not yet: − 12 is still with x.

How do we remove it?

3 Remove the − 12

To remove − 12, we add 12.

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

2x ~~− 12 + 12~~ = 10 + 12

− 12 and + 12 cancel each other.

They make zero.

10 + 12 = 22.

10 + 12 = 22

Now we have 2x = 22.

2x = 22

So after step 3: we added 12, and now we have 2x = 22.

← step 3: added 12

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.

2x2 = 222

2 divided by 2 is 1.

They cancel each other.

So just x is left.

22 divided by 2 is 11.

222 = 11

So x = 11!

x = 11

5 Check

Let's check: put 11 in place of x.

First the left side.

Left: 6(11 − 2) = 6(9) = 54

Now the right side.

Right: 4(11) + 10 = 44 + 10 = 54

Both sides are 54.

So x = 11 is right!

Both sides equal 54

6 Pick the choice

Our answer is x = 11.

That is choice D.

D) 11

7 Why not the others

A is −1.

Wrong: took 12 away instead of adding it: 2x = −2.

A) −1 ✗ took 12 away instead of adding it: 2x = −2

B is 2.2.

Wrong: added 4x instead of taking it away: 10x = 22.

B) 2.2 ✗ added 4x instead of taking it away: 10x = 22

C is 6.

Wrong: 6 × (−2) is −12: the 6 multiplies the 2 too.

C) 6 ✗ 6 × (−2) is −12: the 6 multiplies the 2 too

Let's look back.

First: open the brackets.

Then: get x on one side.

Then: remove the − 12.

Then: remove the 2.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer