How to write an inequality

This lesson will show you how to write an inequality to describe a real-world situation.

Key words to keep in mind.

At most means " no more than, "  " less than or equal to, " or " not greater than"

At least means " no less than " or " greater than or equal to "

Now, let us practice by writing inequalities for the following situations.

Example #1

Suppose a low-sodium food has at most 140 mg per serving.

Solution

Let s = number of milligrams of sodium in a serving of low-sodium food.

Then, s ≤ 140


Example #2

The height of a human being is not greater than 10 feet.

Solution

Let h be the height of a human being

Then, h ≤ 10


Example #3


Foods with high amount of fiber have at least 5 g of fiber per serving. 

Solution

Let f be number of grams of fiber in High-fiber foods.

Then, f ≥ 10


Example #4


Alfred's weekly income is at least 500 dollars with a fixed income of 200 dollars for working at the bank and making 12 dollars and hour  at another job.

Solution

Let x be the number of hours worked weekly.

Fixed income + variable income ≥ 500

200 + 12x ≥ 500




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