Step by step
The question
Question: Kim has 40 points.
She gets 6 points for each level.
She needs at least 100 points.
How many levels must she finish?
1 Find what we know
What do we know?
At least 100 points.
6 points for each level.
At the start: 40 points.
What do we want?
How many levels.
2 Name the unknown
We don't know how many levels.
So we call it x.
At least 100 points means 100 points or more.
We write ≥ 100 points.
3 Write the inequality
In words: what the levels add, plus the start, is at least 100 points.
So the inequality is 6x + 40 ≥ 100.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 6 and + 40.
The + 40 is on the outside, so it comes off first.
Then the times 6.
4 Remove the + 40
To remove + 40, we take away 40.
We do it on both sides, so the sign stays true.
+ 40 and − 40 make zero.
Cross them out.
100 − 40 = 60.
Now we have 6x ≥ 60.
5 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so the sign stays true.
6 divided by 6 is 1.
So just x is left.
60 divided by 6 is 10.
So x is greater than or equal to 10.
6 Show it on a number line
7 Answer the question
Levels come in whole numbers.
10 is a whole number, so it stays.
Careful!
At least 100 points: exactly 100 points is still OK.
So 10 levels is fine.
So at least 10 levels.
8 Check
Let's check in the story.
10 levels: 100 points.
That is at least 100 points.
But 9 levels would be 94 points: not enough.
So 10 is the fewest.
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.