Step by step
The question
Question: simplify 5(x − 2) − 3x.
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 5 in front of the bracket multiplies every part inside.
So we write 5 times each part.
Watch the signs.
5 times x is 5x.
5 times (−2) is −10.
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.
Each colour is one kind.
We move like terms next to each other.
Each term takes its sign with it.
5x − 3x is 2x.
It is like 5 apples take away 3 apples: that is 2 apples.
So the expression is 2x − 10.
3 Check
Let's check.
We pick a small number for each letter: x = 3.
Any number works, and a small one keeps the sums easy.
We put it into the question.
Now into our answer.
Both give −4.
Same value, so 2x − 10 is right!
4 Pick the choice
Our answer is 2x − 10.
That is choice B.
5 Why not the others
A is 2x − 2.
Wrong: 5 × (−2) is −10, not −2.
C is 8x − 10.
Wrong: 5x + 3x: added instead of taking away.
D is 2x + 10.
Wrong: 5 × (−2) is −10, not +10.
Let's look back.
First: open the brackets.
Then: group like terms.
Then: check.
Then: pick the choice.
Last: why not the others.