Question

You need at least $40 to buy some notebooks, but your parents don’t want to give you more than $50. Write an inequality representing the possible amount of money you could get.

Answer 1

m = amount of money you receive

You need at least $40, so that means you need m = 40 or more

So
`m \ge 40` which is the same as saying
`40 \le m`. You flip both sides and also flip the inequality sign as well.

At the same time, your parents won't give you more than $50. So the largest m can get is m = 50. This means
`m \le 50`

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Combine
`40 \le m` and
`m \le 50` to get the compound inequality
`40 \le m \le 50`

This represents all the possible values of m. We see that m can get as small as m = 40, or as large as m = 50, or anything in between.

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Answer:
`40 \le m \le 50`