Step by step
The question
Question: are −2(x − 5) and −2x + 10 equivalent?
−2(x − 5) and −2x + 10
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: −2(x − 5).
We write it shorter, with the same value.
= −2(x − 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.
= (−2)(x) + (−2)(−5)
− × − = +
Watch the signs.
(−2) times x is −2x.
(−2) times (−5) is 10.
= −2x + 10
2 Compare
Now both are −2x + 10.
The same terms.
= −2x + 10 = −2x + 10
So yes: they are equivalent.
= yes: equivalent
3 Check
Let's check with a number: x = 2.
The first gives 6.
The second gives 6.
The same.
So the answer is right!
x = 2: −2(2 − 5) = 6, −2(2) + 10 = 6
Let's look back.
First: open the brackets.
Then: compare.
Last: check.
Answer
= yes: equivalent