Step by step
The question
Question: simplify 4(x + 2) − 2(x − 3).
Simplify means: write it shorter, with the same value.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Open the brackets
The minus sign in front of the 2 goes with it.
So we multiply by −2.
What is in front of a bracket multiplies every part inside.
So we write each part times what is in front.
Watch the signs.
4 times x is 4x.
4 times 2 is 8.
(−2) times x is −2x.
(−2) times (−3) is 6.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
Plain numbers go together.
Each colour is one kind.
We move like terms next to each other.
Each term takes its sign with it.
4x − 2x is 2x.
It is like 4 apples take away 2 apples: that is 2 apples.
8 + 6 is 14.
So the expression is 2x + 14.
3 Check
Let's check.
We pick a small number for each letter: x = 2.
Any number works, and a small one keeps the sums easy.
We put it into the question.
Now into our answer.
Both give 18.
Same value, so 2x + 14 is right!
4 Pick the choice
Our answer is 2x + 14.
That is choice C.
5 Why not the others
A is 2x + 2.
Wrong: −2 × (−3) is +6, not −6.
B is 2x + 5.
Wrong: forgot to multiply the numbers: 4 × 2 and −2 × (−3).
D is 6x + 2.
Wrong: 4x + 2x: added instead of taking away.
Let's look back.
First: open the brackets.
Then: group like terms.
Then: check.
Then: pick the choice.
Last: why not the others.