Step by step
The question
Question: Pens cost $3 and books cost $7.
Omar must spend at least $50.
Write the inequality.
1 Find what we know
What do we know?
Pens cost $3 each.
Books cost $7 each.
Omar must spend $50 or more.
What do we want?
An inequality for this story.
2 Name the unknowns
We don't know how many pens.
We call that number x.
We don't know how many books either.
It is a different number, so it gets its own letter: y.
3 Write the inequality
One pen costs $3.
So x pens cost 3 times x: 3x.
One book costs $7.
So y books cost 7 times y: 7y.
At least $50 means $50 or more.
That is the sign more than or equal to.
In words: the pen money plus the book money is at least $50.
So the inequality is 3x + 7y ≥ 50.
Careful!
At least means 50 or more.
So the sign is more than or equal to, not less than.
4 Check
Let's test it with two buys: a small one and a big one.
1 pen and 1 book cost $10.
That is less than $50, and the inequality says false.
17 pens cost $51.
That is at least $50, and the inequality says true.
Both match the story.
It works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the inequality.
Last: check.