Step by step
The question
Question: simplify −2(3x − 4) + 7.
Simplify means: write it shorter, with the same value.
−2(3x − 4) + 7
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.
= (−2)(3x) + (−2)(−4) + 7
− × − = +
Watch the signs.
(−2) times 3x is −6x.
(−2) times (−4) is 8.
= −6x + 8 + 7
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
Each colour is one kind.
like terms = same letters,
same powers
8 + 7 is 15.
8 + 7 = 15
So the expression is −6x + 15.
= −6x + 15
3 Check
Let's check.
We pick a number for each letter: x = 2.
We put it into the start.
Start: −2 × (3 × 2 − 4) + 7 = −2 × 2 + 7
= −4 + 7 = 3
Now into our answer.
Answer: −6 × 2 + 15 = −12 + 15 = 3
Both give 3.
Same value, so −6x + 15 is right!
Both give 3
Let's look back.
First: open the brackets.
Then: group like terms.
Last: check.
Answer
= −6x + 15