How to write an inequality

This lesson will show you how to write an inequality to describe a real-world situation or when a statement is given.

A few key words to keep in mind.

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

The math symbol that you will use for at most is  ≤ 

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

The math symbol that you will use for at least is  ≥

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

How to write an inequality : easy examples

Example #1

Suppose a low-sodium food has at most 140 mg per serving. Write an inequality that models this situation.

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. Write an inequality that models this situation.

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. Write an inequality that models this situation.

Solution

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

Then, f ≥ 5

How to write an inequality : hard examples

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 per hour at another job. Write an inequality that can model this situation.

Solution

Let x be the number of hours that Alfred worked weekly.

Fixed income + variable income ≥ 500

200 + 12x ≥ 500

Example #5

According to fire laws, a restaurant located on Jefferson's street can have no more than 75 people in it at one time. At the moment, there are 30 people in the restaurant, to include those eating a meal. Write an inequality that models this situation.

Solution

The number of people that can still come inside the restaurant plus the number of people that are already inside the restaurant cannot be more than 75.

We can let x be the number of people who can still come inside the restaurant.

x + 30 ≤ 75