Step by step
The question
Question: 3 more than 4 times a number is 31.
Find the number.
1 Find what we know
What do we know?
3 more than 4 times a number is 31.
What do we want?
The number.
2 Name the unknown
We don't know the number.
So we call it x.
Let's draw it.
The number goes in.
We don't know it yet.
Times 4.
Add 3.
It comes out as 31.
3 Write the equation
Change the words to math, one part at a time.
We start with 4 times a number, then add 3.
So the equation is 4x + 3 = 31.
Now we solve it.
We want x by itself.
First we remove the + 3, so 4x is alone.
Then we remove the times 4.
Is x alone now?
Not yet: + 3 is still with x.
How do we remove it?
4 Remove the + 3
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 cancel each other.
They make zero.
31 − 3 = 28.
Now we have 4x = 28.
So after step 4: we took away 3, and now we have 4x = 28.
Is x alone now?
Not yet: 4x means 4 times x.
5 Remove the 4
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
So just x is left.
28 divided by 4 is 7.
So x = 7.
6 Answer the question
The number is 7.
7 Check
Let's check in the story.
Put 7 in the story: 3 more than 4 times 7.
It makes 31, like the story says.
Check it with the picture.
Put 7 in: 28, then 31.
It comes out as 31.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.