1. Solving Inequalities

2. Standard A.RE1.3 (DOK 1) – Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3. Lesson Essential Question How does the graph of a number line relate to the solution of an inequality?

4. Warm-Up

5. Warm-Up Work

6. Activator For each slide that appears, you will need to use your dry erase marker and plate/board to write what you think the answer is. When I say “GO”, each person needs to hold up their plate with the answer they believe to be true. We want to see what you know on your on not what your neighbor or classmates know. So, go with your gut and don’t look around at others’ answers!

7. Think-Ink-Pair-Share Draw a Venn diagram in your notes. Label one circle “Equation” and the other circle “Inequality”. Think about anything and everything you know about these two concepts and write down the information in the appropriate circle (or in the middle). When I say so, you will talk to your neighbor about what you both wrote down. If they have something you don’t and you both agree that it belongs on the diagram then add it to yours. Likewise, if you believe that they have something that is in the wrong spot after you have discussed it, then decide where the right spot is for it. We will then discuss and share out our answers as a class to see what we can collectively come up with.

8. Venn Diagram

9. Solving Inequalities We want to isolate the __________ in the inequality. We use ____________ _____________ to do so through “undoing” what is being done to the _____________.

10. 4y – 3 < 13

11. 2x – 1 > 6x + 2

12. 2x + 10 ≥ 7(x + 1)

13. Summarizer On a sheet of paper, explain what the difference is between an equation and inequality. Give detailed explanations to where anyone who is not in this class could read your writing and understand exactly what the difference is between these two concepts.

14. Standard A.RE1.3 (DOK 1) – Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

15. Lesson Essential Question How does the graph of a number line relate to the solution of an inequality?

16. Warm-Up

17. Warm-Up Work

18. What happens when… Solve the following: o -2x < -14

19. What happens when… Solve the following: o 10 – c ≥ 6

20. Rule!! When you divide or multiply by a negative number while solving inequalities you must ____________ the inequality symbol so that the solution is viable (correct).

21. What’s Next? Now that we know how to solve any inequality thrown at us, we need to know how to justify our process and steps while solving. Justify means to show proof that the steps we took to get our answer are the correct steps that lead us to the viable (correct) answer. We will do this through building a two column proof.

22. Time to use…. Your Foldable!!! Get out the foldable we made in lab class yesterday that has all of the properties of inequalities listed. This will help us as we create our two column proof, because the justifications come from the properties.

23. Two Column Proof Steps to SolvingJustification

24. Two Column Proof Steps to SolvingJustification

25. Paired Practice With your partner you will need to use the dry erase markers and erasers along with your desk tops to create two column proofs for several inequalities. One person will be the solver and solve the inequality step by step on their desk. The other person will then write justifications for each step of the solving on their desk. Discuss the final product with your partner and if you agree that it is correct copy the chart onto your paper. For each new inequality, the partners will switch roles so that both people get practice doing the solving and justifying. You will turn this in for a small grade at the end of class.

26. Practice Problems

27. Summarizer Solve the following two inequalities o You do not need to justify the steps for these two o -5x + 7 ≤ -8 o -2x + 3 > 3x - 8

28. Standard A.RE1.3 (DOK 1) – Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

29. Lesson Essential Question How does the graph of a number line relate to the solution of an inequality?

30. Warm-Up What did we learn the previous two days? o After you have written your answer to the above, look at the graph below and explain anything you know about it or what it tells us.

31. Warm-Up Work

32. Graphing Solutions to Inequalities You may be asking yourself: o How do we know when the circle is open on the solution graph? o How do we know when the circle is closed on the solution graph? o How do we know which way the line on the solution graph faces?

33. Graphing Solutions to Inequalities <>≤≥ Open Circle Closed Circle Solution Line Points Left Solution Line Points Right Solution Line Points Left Solution Line Points Right

34. L eft and L ess Than both start with L ’s o So Less Than and Less Than or Equal to Inequalities have solution lines that point left. o That means that the other two (greater than and greater than or equal to) have solution lines that point right. If you look at it graphically look what happens: o The left arrow looks like the less than sign (<), so the solution lines for any inequalities with less than or less than or equal to point left. o The right arrow looks like the greater than sign (>), so the solution lines for any inequalities with greater than or greater than or equal to point right. Here’s How to Remember It!!!

35. Greater than or equal to (≥) and Less than or equal to (≤) both have the “equal line” under them. o This means that the solutions to these two types of inequalities INCLUDE the number being related to x For example, if the solution is x ≥ 6, then the solutions are any number greater than 6 but also 6 itself! Therefore, when we graph inequalities with greater than OR EQUAL TO and less than OR EQUAL TO we have to include the number the dot lies on. So these solutions have to have closed circles whereas the solutions to less than or greater than are open circles because we don’t include the number the dot lies on in the solution graph.

36. Placemat Activity Let’s Practice! In groups of 4 you will complete a placemat illustrating everything we have learned over the past few days about solving inequalities. You will divide your paper into four sections. Each person will start out with a given inequality that needs to be solved. You will complete step one of solving your inequality, but then you will rotate the placemat so that you are completing the next step of another problem. This rotation process will continue until all 4 problems are completely solved. On the problem you end up writing the final solution for, you will also be graphing the solution on a number line. Your group will then continue the rotation process until all 4 problems have been fully justified for each step in the solving process your group took.

37. Summarizer 3-2-1 3 – Write three things you know about solving or graphing inequalities 2 – Solve and graph the following 2 inequalities o 12(x + 2) < 48 o -2x +12 ≥ 36 1 – Answer the lesson essential question o How does the graph of a number line relate to the solution of an inequality?