Step by step
The question
Question: A plumber charges $40 plus $30 per hour.
Dan can pay at most $160.
How many hours can the plumber work?
1 Find what we know
What do we know?
At most $160.
$30 for each hour.
$40 one time.
What do we want?
How many hours.
2 Name the unknown
We don't know how many hours.
So we call it x.
At most $160 means $160 or less.
We write ≤ $160.
3 Write the inequality
In words: what the hours add, plus the start, is at most $160.
So the inequality is 30x + 40 ≤ 160.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 30 and + 40.
The + 40 is on the outside, so it comes off first.
Then the times 30.
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.
160 − 40 = 120.
Now we have 30x ≤ 120.
5 Remove the 30
30x means 30 times x.
We want just x.
To remove times 30, we divide by 30.
We do it on both sides, so the sign stays true.
30 divided by 30 is 1.
So just x is left.
120 divided by 30 is 4.
So x is less than or equal to 4.
6 Show it on a number line
7 Answer the question
Hours come in whole numbers.
4 is a whole number, so it stays.
Careful!
At most $160: exactly $160 is still OK.
So 4 hours is fine.
So at most 4 hours.
8 Check
Let's check in the story.
4 hours: $160.
That is not more than $160.
But 5 hours would be $190: too much.
So 4 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.