Step by step
The question
Question: simplify 3x + 2(x − 4) − 5.
Simplify means: write it shorter, with the same value.
3x + 2(x − 4) − 5
1 Open the brackets
The 2 in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write 2 times each part.
= 3x + 2(x) + 2(−4) − 5
− × + = −
Watch the signs.
2 times x is 2x.
2 times (−4) is −8.
= 3x + 2x − 8 − 5
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.
like terms = same letters,
same powers
3x + 2x is 5x.
It is like 3 apples plus 2 apples: that is 5 apples.
−8 − 5 is −13.
3x + 2x = 5x
−8 − 5 = −13
So the expression is 5x − 13.
= 5x − 13
3 Check
Let's check.
We pick a number for each letter: x = 2.
We put it into the start.
Start: 3 × 2 + 2 × (2 − 4) − 5
= 6 + 2 × (−2) − 5 = 6 + (−4) − 5
= 6 − 4 − 5 = −3
Now into our answer.
Answer: 5 × 2 − 13 = 10 − 13 = −3
Both give −3.
Same value, so 5x − 13 is right!
Both give −3
Let's look back.
First: open the brackets.
Then: group like terms.
Last: check.
Answer
= 5x − 13