1. Chapter 5 Notes
Algebra I

2. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Inequality – Addition Property of Inequalities Words: Symbols:

3. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Inequality – A mathematical sentence that contains < , > , < , or > Addition Property of Inequalities Words: Any number is allowed to be added to both sides of a true inequality Symbols: If a > b, then a + c > b + c If a < b, then a + c < b + c

4. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Graphing inequalities on a number line:
Put a circle on the _____________ point
Fill the circle in if the sign is _______ or _______
Leave the circle open if the sign is _____ or ____
Shade the left side if the variable is ____________ to the number
Shade the right side if the variable is ____________ to the number
Ex) Graph x < Ex) Graph 4 < x

5. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) x – 12 > 8 2) 22 > x – 8 3) x – 14 < -19

6. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Subtraction Property of Inequalities Words: Symbols:

7. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Subtraction Property of Inequalities Words: Any number is allowed to be subtracted from both sides of a true inequality Symbols: If a > b, then a – c > b – c If a < b, then a – c < b – c

8. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) x + 19 > 56 2) 18 > x + 8 3) 22 + x < 5

9. Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) 3x + 6 < 4x 2) 10x < 9n – 1

10. Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 1 Words: Symbols:

11. Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 1 Words: Any positive number is allowed to be multiplied to both sides of an inequality Symbols (c > 0): If a > b, then ac > bc If a < b, then ac < bc

12. Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 2 Words: Symbols:

13. Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 2 Words: Any negative number is allowed to be multiplied to both sides of an inequality, as long as the sign gets flipped! Symbols (c < 0): If a > b, then ac < bc If a < b, then ac > bc

14. Section 5-2: Solving Inequalities by Multiplication and Division
Solve 1) 2) 3) 4)

15. Section 5-2: Solving Inequalities by Multiplication and Division
Division Property of Inequalities: Part 1 Words: Any positive number is allowed to be divided to both sides of an inequality Symbols (c > 0): If a > b, then If a < b, then

16. Section 5-2: Solving Inequalities by Multiplication and Division
Division Property of Inequalities: Part 2 Words: Any negative number is allowed to be divided to both sides of an inequality, as long as the sign gets flipped! Symbols (c < 0): If a > b, then If a < b, then

17. Section 5-2: Solving Inequalities by Multiplication and Division
Solve and graph the solution set 1) 4x > 16 2) -7x < 147 3) -15 < 5x 4) -20 > -10x

18. Section 5-3: Solving Multi-Step Inequalities
Solve the following multi-step inequalities. Graph the solution set. 1) -11x – 13 > 42 2) x < 31 3) 23 > 10 – 2x

19. Section 5-3: Solving Multi-Step Inequalities
Solve the following multi-step inequalities. Graph the solution set.
4(3x – 5) + 7 > 8x + 3
2(x + 6) > -3(8 – x)

20. Section 5-3: Solving Multi-Step Inequalities
Translate the verbal phrase into an expression and solve Five minus 6 times a number n is more than four times the number plus 45

21. Section 5-3: Solving Multi-Step Inequalities, SPECIAL SOLUTIONS
Solve the following inequalities. Indicate if there are no solutions or all real number solutions.
1) 9x – 5(x – 5) < 4(x – 3) 2) 3(4x + 6) < (2x – 4)

22. Day 1, Section 5-4: Compound Inequalities
Compound Inequality – two inequalities combined into one with an overlapping solution set And vs. Or Graph Graph Inequality Inequality Intersection Union

23. Day 1, Section 5-4: Compound Inequalities (ANDs)
Ex) Graph the intersection of the two inequalities and write a compound inequality for x > 3 and x < 7 Ex) Solve and graph -2 < x – 3 < 4

24. Day 1, Section 5-4: Compound Inequalities (ANDs)
Solve the following inequalities and graph the solution set on a number line Ex) y – 3 > -11 and y – 3 < -8 Ex) 6 < r + 7 < 10

25. Day 2, Section 5-4: Compound Inequalities (ORs)
Graph the following inequalities on the same number line: x > 2 or x < -1 Ex) Solve and graph the solution set for: -2x + 7 < 13 or 5x + 12 > 37

26. Day 2, Section 5-4: Compound Inequalities (ORs)
Solve the following inequalities and graph the solution set
a + 1 < ) x < 9 or 2 + 4x < 10
Or a – 1 > 3

27. Day 1, Section 5-5 Absolute Value Inequalities (distance is “less than”
What does mean? Absolute value inequalities that have _______ or _________ symbols are treated like _______ problems!! The solution set will be an _____________.

28. Day 1, Section 5-5 Absolute Value Inequalities (distance is “less than”)
What does mean? The distance from zero on the number line is less than 3. Absolute value inequalities that have less than (<) or less than or equal (<) to symbols are treated like AND problems!! The solution set will be an intersection.

29. 5-4: Steps for Solving Abs. Value Inequalities: or
1) Re-write as an AND problem with boundaries +c and –c. (Lose the abs. value symbols) 2) Solve the AND problem 3) Graph the solution
Ex)

30. Day 1, Section 5-5 Absolute Value Inequalities (distance is “less than”)
Solve the following absolute value problems. Graph the solution set. 1) 2) 3) 4)

31. Day 2, Section 5-5 Absolute Value Inequalities(distance is “greater than”)
What does mean? Absolute value inequalities that have _______ or _________ symbols are treated like _______ problems!! The solution set will be a _____________.

32. Day 2, Section 5-5 Absolute Value Inequalities(distance is “greater than”)
What does mean? The distance from 0 on the number line is greater than 3 Absolute value inequalities that have greater than (>) or greater than or equal to (>) symbols are treated like OR problems!! The solution set will be a union.

33. 5-4: Steps for Solving Abs. Value Inequalities: or
1) Re-write as an OR problem. Split into 2 problems, one with +c and one with –c (Lose the abs. value symbols) ***YOU MUST FLIP SIGN ON –C PROBLEM 2) Solve the two problems 3) Graph the solution
Ex)

34. Day 2, Section 5-5 Absolute Value Inequalities(distance is “greater than”)
Solve the following absolute value inequalities 1) 2) 3) 4)

35. Section 5-6: Graphing Linear Inequalities
Linear Equations vs.
Linear Inequalities
Plot any 2 points
Draw a solid line through the 2 points
Put in slope-int form first
Plot any two points
Determine whether to connect the points with a solid OR dashed line
Shade ONE side of the line
You must determine which side
You shade the solution set!

36. Section 5-6: Graphing Linear Inequalities
Steps for graphing linear inequalities:
Plot 2 points on the line
If the symbol is < or > connect with a dashed line
If the symbol is < or >, connect with a solid line
Shade above the line for
y > mx + b (or >)
5) Shade below the line for
y < mx + b (or <)
Ex. Graph y < 2x – 4

37. Section 5-6: Graphing Linear Inequalities
Graph the following linear inequalities Ex) Ex) y < x – 1

38. Section 5-6: Graphing Linear Inequalities
Graph the following linear inequalities Ex) 3x – y < 2 Ex) x + 5y < 10