Step by step
The question
Question: solve 5x + 8 = 43.
Let's find x.
We want x by itself.
First we remove the + 8, so 5x is alone.
Then we remove the times 5.
There are four choices.
First we solve it, the normal way.
Then we pick.
Is x alone now?
Not yet: + 8 is still with x.
How do we remove it?
1 Remove the + 8
To remove + 8, we take away 8.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
+ 8 and − 8 cancel each other.
They make zero.
43 − 8 = 35.
Now we have 5x = 35.
So after step 1: we took away 8, and now we have 5x = 35.
Is x alone now?
Not yet: 5x means 5 times x.
2 Remove the 5
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
They cancel each other.
So just x is left.
35 divided by 5 is 7.
So x = 7!
3 Check
Let's check: put 7 in place of x.
We get 43, the same as the right side.
So x = 7 is right!
4 Pick the choice
Our answer is x = 7.
That is choice A.
5 Why not the others
B is 51/5.
Wrong: added 8 instead of taking it away: 5x = 51.
C is 35.
Wrong: 5x = 35, but we still had to divide by 5.
D is 175.
Wrong: 35 × 5: multiplied instead of dividing.
Let's look back.
First: remove the + 8.
Then: remove the 5.
Then: check.
Then: pick the choice.
Last: why not the others.