Step by step
The question
Question: if 7x − 7 = −21, what is x − 1?
We want x − 1.
Let's look for it inside the equation.
1 Compare the two
Look at 7x − 7 and x − 1.
We compare them part by part.
7x is 7 times x.
7 divided by 1 is 7.
So 7 is 7 times 1.
Every part of 7x − 7 is 7 times a part of x − 1.
2 Take out the 7
So we can write each part as 7 times.
7 times each part is the same as 7 times the whole bracket: 7(x − 1).
Opening the bracket gives 7x − 7 back.
3 Remove the 7
7(x − 1) means 7 times the bracket.
To remove times 7, we divide by 7.
We do it on both sides, so they stay equal.
7 divided by 7 is 1.
So just the bracket is left.
−21 divided by 7 is −3.
So x − 1 = −3!
Careful!
Many people find x and stop.
But the question asks for x − 1.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 7 and − 7.
First x was times 7.
Then − 7.
To take them off, we go backwards.
First we remove the − 7.
Then the times 7.
To remove − 7, we add 7.
We do it on both sides, so they stay equal.
− 7 and + 7 make zero.
Cross them out.
−21 + 7 = −14.
Now we have 7x = −14.
7x means 7 times x.
We want just x.
To remove times 7, we divide by 7.
We do it on both sides, so they stay equal.
7 divided by 7 is 1.
So just x is left.
−14 divided by 7 is −2.
So x = −2!
Then x − 1 is (−2) − 1 = −2 − 1 = −3.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 7.
Then: remove the 7.
Last: check.