Step by step
The question
Question: A shelf can hold up to 30 kg.
Each pot weighs 4 kg.
How many pots can it hold?
1 Find what we know
What do we know?
Up to 30 kg.
4 kg for each pot.
What do we want?
How many pots.
2 Name the unknown
We don't know how many pots.
So we call it x.
Up to 30 kg means 30 kg or less.
We write ≤ 30 kg.
3 Write the inequality
In words: what the pots make is up to 30 kg.
So the inequality is 4x ≤ 30.
Now we solve it.
4 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so the sign stays true.
4 divided by 4 is 1.
So just x is left.
We can make 30/4 simpler.
It is the same as 15/2.
So x is less than or equal to 15/2.
5 Show it on a number line
6 Answer the question
15/2 is 7.5.
Pots come in whole numbers.
The biggest whole number up to 7.5 is 7.
So we round down.
Careful!
7.5 rounds to 8 the usual way.
But 8 pots are 32 kg.
That is too much.
So we round down.
So at most 7 pots.
7 Check
Let's check in the story.
7 pots: 28 kg.
That is not more than 30 kg.
But 8 pots would be 32 kg: too much.
So 7 is the most.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the inequality.
Then: solve it.
Then: answer the question.
Last: check.