1. Solve Inequalities Using Addition and Subtraction
Section 6-1
Solve Inequalities Using Addition and Subtraction
Objective: Students will create and solve inequalities.
Standards: A.REI.1 , A.REI.3 , A.CED.3

2. Graph of an inequality: The set of points that represent all solutions of the inequality.
< or > Open Circle on Graph
≤ or ≥ Closed Circle on Graph

3. < ≤ > ≥ REVIEW: Fewer than Is less than At most, no more than
Symbol
Meaning
Example
<
Fewer than
Is less than
Is less than or equal to ≤
At most, no more than
>
Is greater than
More than
Is greater than or equal to ≥
At least, no less than

4. Example 1
Graph:
x < 4
x ≥ -1

5. Example 2 Write an inequality represented by the graph. -3 -2 -1 0 1 2
x ≤ -1.5
(The inequality points the SAME DIRECTION as the ARROW. But must have variable on LEFT side for this to work!)

6. Example 3 Solve an inequality using addition: JUSTIFY m – 3.8 < -1
m < 2.8
Graph:
Given
Addition Property of Inequality
Simplify

7. Example 4 Solve an inequality using subtraction: 3 ≤ b + 7 b + 7 ≥ 3
b ≥ -4
Graph:
If variable is on “wrong” side FLIP the WHOLE inequality!
Given
Symmetric
APOI
Simplify

8. Homework Section 6.1 Pg 359 – 361 4 – 8 SOLVE & PROVE: 10, 11, 14- 17,
Follow Directions: 31, 32, 34

9. Solve Inequalities Using Multiplication and Division
Section 6-2
Solve Inequalities Using Multiplication and Division
Objective: Students will create and solve inequalities.
Standards: A.REI.1 , A.REI.3 , A.CED.3

10. When multiplying or dividing by a NEGATIVE number – you Reverse or Flip the inequality symbol.

11. < ≤ > ≥ REVIEW: Fewer than Is less than At most, no more than
Symbol
Meaning
Example
<
Fewer than
Is less than
Is less than or equal to ≤
At most, no more than
>
Is greater than
More than
Is greater than or equal to ≥
At least, no less than

12. Example 1 Solve an inequality using multiplication: y ≥ -4 y ≥ -28 7
Graph:
Given
Multiplication Property of Inequality (MPOI)
y ≥ -28
Simplify

13. Example 2 Solve an inequality using multiplication: x > -2 x < 6-3
-3 • x > -2 • -3
Graph:
Given
MPOI
Flip inequality – multiplied by a negative.
x < 6
Simplify

14. Example 3 ≥ Solve an inequality using division: 18 ≤ -6x x ≤ -3 -6x 18
Graph:
Given
SWITCH so x on left side ≥
Symmetric
MPOI
Flip inequality – divided by a negative.
Simplify
x ≤ -3

15. Homework
Section 6.2
Pg 366 – 368
Solve & Prove: 3, 7, 11, 15, 19, 23,
Follow Directions: 36, 37, 39