Lesson 16Interpreting Inequalities

Learning Goal

Let’s write inequalities.

Learning Targets

  • I can match an inequality to a situation it represents, solve it, and then explain what the solution means in the situation.

  • If I have a situation and an inequality that represents it, I can explain what the parts of the inequality mean in the situation.

Lesson Terms

  • solution to an inequality

Warm Up: Solve Some Inequalities!

Problem 1

For each inequality, find the value or values of that make it true.

Activity 1: Club Activities Matching

Problem 1

Choose the inequality that best matches each given situation. Explain your reasoning.

  1. The Garden Club is planting fruit trees in their school’s garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need pound fertilizer each.

  2. The Chemistry Club is experimenting with different mixtures of water with a certain chemical (sodium polyacrylate) to make fake snow.
    To make each mixture, the students start with some amount of water, and then add of that amount of the chemical, and then 9 more grams of the chemical. The chemical is expensive, so there can’t be more than a certain number of grams of the chemical in any one mixture.

  3. The Hiking Club is on a hike down a cliff. They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute.

  4. The Science Club is researching boiling points. They learn that at high altitudes, water boils at lower temperatures. At sea level, water boils at . With each increase of 500 feet in elevation, the boiling point of water is lowered by about .

Activity 2: Club Activities Display

Problem 1

Your teacher will assign your group one of the situations from the last task. Create a visual display about your situation. In your display:

  • Explain what the variable and each part of the inequality represent

  • Write a question that can be answered by the solution to the inequality

  • Show how you solved the inequality

  • Explain what the solution means in terms of the situation

Are you ready for more?

Problem 1

is a set of four consecutive integers whose sum is 18.

  1. How many sets of three consecutive integers are there whose sum is between 51 and 60? Can you be sure you’ve found them all? Explain or show your reasoning.

  2. How many sets of four consecutive integers are there whose sum is between 59 and 82? Can you be sure you’ve found them all? Explain or show your reasoning.

Lesson Summary

We can represent and solve many real-world problems with inequalities. Writing the inequalities is very similar to writing equations to represent a situation. The expressions that make up the inequalities are the same as the ones we have seen in earlier lessons for equations. For inequalities, we also have to think about how expressions compare to each other, which one is bigger, and which one is smaller. Can they also be equal?

For example, a school fundraiser has a minimum target of $500. Faculty have donated $100 and there are 12 student clubs that are participating with different activities. How much money should each club raise to meet the fundraising goal? If is the amount of money that each club raises, then the solution to is the minimum amount each club has to raise to meet the goal. It is more realistic, though, to use the inequality since the more money we raise, the more successful the fundraiser will be. There are many solutions because there are many different amounts of money the clubs could raise that would get us above our minimum goal of $500.