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Matching Representations of Inequalities

2.13.3 Matching Representations of Inequalities

2.13.3 • Matching Representations of Inequalities

Activity

Your teacher will give you a set of cards. Take turns with your partner to match a group of 4 cards that contain: a situation, an inequality that represents it, a graph that represents the solution region, and a solution written as a coordinate pair.

For each match that you find, explain to your partner how you know it's a match.

For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

Record your matches.

Group 1

  • situation: perimeter of a rectangle
  • inequality:
  • a solution:
  • sketch of graph:

Group 2

  • situation: jar of coins
  • inequality:
  • a solution:
  • sketch of graph:

Group 3

  • situation: honey and jam
  • inequality:
  • a solution:
  • sketch of graph:

Group 4

  • situation: a school trip
  • inequality:
  • a solution:
  • sketch of graph:

Compare your answer: Your answer may vary, but here is a sample.

Group 1 - situation: perimeter of a rectangle               Group 2 - situation: jar of coins

Card Sort: Representations of Inequalities blackline masters

           Group 3 - situation: honey and jam                  Group 4 - situation: a school trip

Card Sort: Representations of Inequalities blackline masters

Self Check

Veronica works two part time jobs in order to earn enough money to meet her obligations of at least $280 a week. Her job at the day spa pays $10 an hour and her administrative assistant job on campus pays $17.50 an hour. 

Which of the following is a solution that allows Veronica to earn enough money?

  1. 5 hours at the day spa and 15 hours as an administrative assistant
  2. 15 hours at the day spa and 5 hours as an administrative assistant
  3. 10 hours at the day spa and 10 hours as an administrative assistant

  4. 5 hours at the day spa and 10 hours as an administrative assistant


Additional Resources

Connecting Representations of Inequalities

In order to connect the constraints of a situation with an inequality, its graph, and possible solutions, we need a mastery of each representation.

Example

Christy sells her photographs at a booth at a street fair. Each small photo she displays costs her $4 and each large photo costs her $10. She doesn’t want to spend more than $200 on photos to display.

Let xx be the number of small photos and yy be the number of large photos that Christy displays.

We know that each small photo costs $4 to display and each large photo costs $10. We also know that she doesn’t want to spend more than $200.

The inequality that represents this situation is 4x+10y≤2004x+10y≤200.

To be able to connect this inequality with possible solutions, translating it into a graph is an important step.

Try it

Connecting Representations of Inequalities

1.

Graph the linear inequality: 4x+10y≤2004x+10y≤200.

Compare your answer:

Graph of an inequalilty on the coordinate plane.
2.

Is it possible for Christy to display 15 small paintings and 15 large paintings and maintain her budget of $200?

Compare your answer:

No; the ordered pair (15,15)(15,15) does not fall within the region representing the solution. Another way to verify this is by using the inequality.

4x+10y≤2004(15)+10(15)≤20060+150≤200210≰2004x+10y≤2004(15)+10(15)≤20060+150≤200210≰200

Since $210 is not less than $200, 15 small paintings and 15 large paintings does not stay with Christy’s budget of $200.