1. Solving Linear Inequalities
Chapter 2

2. Writing and Graphing Inequalities
I can write and graph linear inequalities.

3. Writing and Graphing Inequalities
Vocabulary (page 30 in Student Journal)
inequality: a mathematical sentence that uses a symbol to compare expressions that are not always equal
solution set: set of all solutions to an inequality (typically inequalities will have more than 1 solution)

4. Writing and Graphing Inequalities
Core Concepts (page 30 in Student Journal)
Common inequalities include less than, less than or equal to, greater than, and greater than or equal to.

5. Writing and Graphing Inequalities
Examples (space on page 30 in Student Journal)
Write an inequality to for the scenario below.
a) rides starting at $19.99
b) speed limit 35 miles per hour

6. Writing and Graphing Inequalities
Solutions
a) r greater than or equal to 19.99
b) s less than or equal to 35

7. Writing and Graphing Inequalities
Examples
Determine if the following are solutions to the inequality y < 6.
c) 0
d) 2

8. Writing and Graphing Inequalities
Solutions
c) no, 13 is not less than 6
d) yes, -1 is less than 6

9. Writing and Graphing Inequalities
Examples
e) Graph -4 > y
f) Write the inequality for the graph.

10. Writing and Graphing Inequalities
Solutions a)
b) x < 12

11. Solving Inequalities Using Addition or Subtraction
I can solve inequalities using addition and subtraction.

12. Solving Inequalities Using Addition or Subtraction
Core Concepts (pages 35 and 36 in Student Journal)
Addition Property of Inequality (a, b and c are real numbers)
If a > b, then a + c > b + c
If a < b, then a + c < b + c

13. Solving Inequalities Using Addition or Subtraction
Subtraction Property of Inequality (a, b and c are real numbers)
If a > b, then a - c > b - c
If a < b, then a - c < b - c

14. Solving Inequalities Using Addition or Subtraction
Examples (space on pages 35 and 36 in Student Journal)
a) Solve n - 5 < -3.
b) Solve -1 > y + 12.

15. Solving Inequalities Using Addition or Subtraction
Solutions
a) n < 2
b) -13 > y or y < -13

16. Solving Inequalities Using Multiplication or Division
I can solve inequalities by multiplying or dividing.

17. Solving Inequalities Using Multiplication or Division
Core Concepts (page 40 in Student Journal)
Multiplication Property of Inequality (a, b and c are real numbers)
If a > b and c > 0, then ac > bc
If a < b and c > 0, then ac < bc
If a > b and c < 0, then ac < bc
If a < b and c < 0, then ac > bc

18. Solving Inequalities Using Multiplication or Division
Division Property of Inequality (a, b and c are real numbers)
If a > b and c > 0, then a/c > b/c
If a < b and c > 0, then a/c < b/c
If a > b and c < 0, then a/c < b/c
If a < b and c < 0, then a/c > b/c

19. Solving Inequalities Using Multiplication or Division
Examples (space on page 40 in Student Journal)
a) what are the solutions to c/8 > ¼ ?
b) what are the solutions to x/-5 < -3

20. Solving Inequalities Using Multiplication or Division
Solutions
a) c > 2
b) x > 15

21. Solving Inequalities Using Multiplication or Division
Examples
c) what are the solutions to 12a < 6 ?
d) what are the solutions to -5y > -10

22. Solving Inequalities Using Multiplication or Division
Solutions
c) a < ½
d) y < 2

23. Solving Multi-Step Inequalities
I can solve multi-step inequalities.

24. Solving Multi-Step Inequalities
Examples (space on page 45 in Student Journal)
Solve the following inequalities.
a) -6a - 7 < 17
b) 15 > 5 - 2(4m + 7)
c) 3b + 12 > b

25. Solving Multi-Step Inequalities
Solutions
a) a > 4
b) -3 < m or m > -3
c) b > 3

26. Solving Compound Inequalities
I can write, graph, and solve compound inequalities.

27. Solving Compound Inequalities
Vocabulary (page 50 in Student Journal)
compound inequality: 2 distinct inequalities joined by the word and or the word or
In order to solve a compound inequality we can take the compound inequality and separate into 2 inequalities and solve them each individually.

28. Solving Compound Inequalities
Examples (space on page 50 in Student Journal)
Write a compound inequality.
a) all real numbers greater than 4 and less than 6
b) all real numbers less than 7 or greater than 12

29. Solving Compound Inequalities
Solutions
4 < x < 6
x < 7 or x > 12

30. Solving Compound Inequalities
Examples
Solve the following inequality.
c) -2 < 3y - 4 < 14

31. Solving Compound Inequalities
Solutions
c) ⅔ < y < 6

32. Solving Absolute Value Inequalities
I can solve absolute value inequalities.

33. Solving Absolute Value Inequalities
Core Concepts (page 55 in Student Journal)
In order to solve an absolute value inequality in the form abs(A) < b, where A is a variable expression and b > 0 we can solve the compound inequality -b < A < b. If the inequality is in the form abs(A) > b we would have to solve the compound inequality A < -b or A > b.

34. Solving Absolute Value Inequalities
Examples (space on page 55 in Student Journal)
Solve the following inequalities.
a) abs(2x + 4) > 5
b) abs(w - 213) < 7

35. Solving Absolute Value Inequalities
Solutions
a) x > .5 or x < -4.5
b) 206 < w < 220