How can you write an inequality to describe a situation? In mathematics, inequalities are a fundamental concept that allows us to compare two quantities and determine their relationship. Whether it’s in real-life scenarios or in mathematical problems, inequalities play a crucial role in solving problems and making decisions. In this article, we will explore the process of writing an inequality to describe a situation, providing examples and explanations along the way.
Inequality is a mathematical expression that compares two quantities using symbols such as “<", ">“, “<=", or ">=”. It helps us understand the relationship between these quantities, whether they are equal, greater than, or less than each other. To write an inequality that accurately describes a situation, we need to identify the quantities involved and determine their relationship.
Let’s consider a simple example. Suppose you are planning a road trip and you want to ensure that your fuel tank has enough fuel to cover the distance. The distance you can travel on a full tank of fuel is 400 miles, and the car’s fuel efficiency is 30 miles per gallon. If you want to make sure you have enough fuel, you can write an inequality to describe this situation.
The quantity we are interested in is the amount of fuel, which we can represent as “x” gallons. The distance you can travel on a full tank of fuel is 400 miles, and the car’s fuel efficiency is 30 miles per gallon. Therefore, the inequality to describe this situation is:
x 30 ≥ 400
This inequality states that the product of the amount of fuel (x) and the car’s fuel efficiency (30 miles per gallon) must be greater than or equal to 400 miles. In other words, you need to have at least 400/30 = 13.33 gallons of fuel to ensure you have enough for the trip.
Now, let’s consider a more complex example. Suppose you are managing a budget for a small business, and you want to ensure that your expenses do not exceed your income. Your monthly income is $5,000, and your monthly expenses include rent ($1,200), utilities ($300), and salaries ($2,000). You can write an inequality to describe this situation as follows:
Income – Rent – Utilities – Salaries ≥ 0
This inequality states that the income minus the expenses (rent, utilities, and salaries) must be greater than or equal to zero. In other words, your income must be sufficient to cover your expenses, ensuring that the business remains profitable.
In conclusion, writing an inequality to describe a situation involves identifying the quantities involved and determining their relationship. By using symbols such as “<", ">“, “<=", or ">=”, we can express the relationship between these quantities and make informed decisions based on the inequality. Whether it’s for a road trip or managing a business budget, inequalities are a powerful tool in mathematics that can help us solve real-life problems.
