## Real World Applications – Algebra I

### Topic

Where do you see compound inequalities in your world?

### Student Exploration

In this activity, we will apply our basic understanding of compound inequalities to things and activities we see around us. In the concept, you learned about two different types of compound inequalities.

An example of a compound inequality involving the word “and” can be thought of as an elevator. An elevator for a building must be greater than (or equal to) floor zero and the top floor. For a 20-floor apartment building with no basement, we can represent the elevator reaching all of the floors between the ground floor and the top floor, or \begin{align*}0 \le x \le 20\end{align*}. In words, we can say that the elevators must be able to reach greater than or equal to the ground floor AND less than or equal to the \begin{align*}20^{th}\end{align*} floor.

An example of a compound inequality involving the word “or” can be thought of a car burning fuel. A car burns more gasoline when it’s going either really slow or really fast. When we look at how the different ways driving a car can be more expensive, a car must be going below 40 miles an hour and higher than 70 miles an hour. The inequality to represent this is the speed is less than 40 miles per hour OR greater than 70 miles per hour. We can say, \begin{align*}x < 40\end{align*} or \begin{align*}x > 70\end{align*}.

### Extension Investigation

Where do you see compound inequalities around you? How could you write the inequality? Which type of wording would you use – “and,” or “or” and why?