1. Chapter 4: Solving Inequalities
4.2 and 4.3
Solving Inequalities Using Addition, Subtraction, Multiplication, and Division

2. Equivalent Inequalities
Inequalities with the same solutions
We create these as we solve equations
Each line is an equivalent inequality to the one before it

3. Addition Property of Inequality
In easier terms:
If you add something to one side of an inequality, you must add it to the other side as well

4. Example 1
Solve x – 3 < 5 and graph the solution.

5. Example 1a
Solve m – 6 > -4 and graph the solution.

6. Example 2
Solve 12 ≤ x – 5 and graph your solution.

7. Example 2a
Solve n – 7 ≤ -2 and graph the solution.

8. Subtraction Property of Inequality
In easier terms:
If you subtract something from one side of an inequality, you must subtract it from the other side also

9. Example 3
Solve y + 5 < -7 and graph the solution.

10. Example 3a
Solve t + 3 ≥ 8 and graph the solution.

11. Example 4
The maximum safe load of a chairlift is 680 lbs. In the spring, a cyclist and bicycle go to the top of the slope using the chairlift. The weight of the person is 124 lbs, and the weight of the bicycle is 32 lbs. Which inequality best describes how much additional weight w the chairlift could safely carry?
124 + w ≤
w ≤ 680
32 + w ≥
w ≥ 680

12. Example 4a
Your baseball team has a goal to collect at least 160 blankets for a shelter. Team members brought 42 blankets on Monday and 65 blankets on Wednesday. Write an inequality to describe how many blankets the team must donate on Friday to make or exceed their goal.

13. Multiplication Property of Inequality for c > 0
IF whatever you’re multiplying by is greater than 0 (positive)
If you multiply one side of an inequality by something, you must multiply the other side by the same thing

14. Example 1
Solve and graph the solution.

15. Example 1a
Solve and graph the solution.

16. Example 1b
Solve and graph the solution.

17. Example 1c
Solve and graph the solution.

18. Multiplication Property of Inequality for c < 0
IF whatever you’re multiplying by is NEGATIVE
You still multiply both sides by that number
BUT, you flip your inequality sign!

19. Example 2
Solve and graph the solution.

20. Example 2a
Solve and graph the solution.

21. Example 2b
Solve and graph the solution.

22. Example 2c
Solve and graph the solution.

23. Example 3
Solve and graph the solution.

24. Example 3a
Solve and graph the solution.

25. Example 3b
Solve and graph the solution.

26. Example 3c
Solve and graph the solution.

27. Example 4
The student council votes to buy food for a local food bank. A case of 12 jars of spaghetti sauce costs $ What is the greatest number of cases of sauce the student council can buy if they use at most $216 for this project?

28. Example 4a
Students in the school band are selling calendars. They earn $.40 on each calendar they sell. Their goal is to earn more than $327. Write and solve an inequality to find the fewest number of calendars they can sell and still reach their goal.

29. Homework P. 208: 4-18 even, 24-38 even, 46, 52, 56, 72