1. Lesson 4: Solving Inequalities

2. Recall: Graphing and Writing an Inequality
Phrase:
“All real numbers less than 2”
Set Notation:
{ x| x < 2, x ε R } 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

3. Recall: Graphing and Writing an Inequality
Phrase:
“All integers greater-than or equal to -4.”
Set Notation:
{x|x > -4, x ε I} 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

4. Recall: Graphing and Writing an Inequality
Phrase:
“All real numbers greater than -3 and less-than or equal to 6.”
Set Notation:
{ x|-3 < x < 6, x ε R} 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

5. Mult/Div Property of inequalities
When you multiply or divide an inequality by a negative value, it changes the direction of the inequality. 
-x > 4 becomes x < -4

6. Solve and Graph Ex 1: 5x + 14 < 29 -14 -14 5x ≤ 15 ___ ___ 5 5
Check:
Ex 1: x + 14 < 29
Pick a value that suits the inequality. For this one, we will use x = 2.
5x + 14 ≤ 29
5(2) + 14 ≤ 29
≤ 29
5x ≤ 15
___ ___
24 ≤ 29 True!
x ≤ 3 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

7. Solve and Graph Ex 2: 25x + 1 < 5x + 41 -5x -5x 20x + 1 < 41
Check:
Let’s use x = 0!
Ex 2: x + 1 < 5x + 41
25x + 1 < 5x + 41
-5x x
25(0) + 1 < 5(0) + 41
0 + 1 <
20x + 1 < 41
1 < TRUE!
20x < 40
___ ___
x < 2 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

8. Solve and Graph Ex 3: -11x – 9 < -42 + 9 + 9 -11x < -33 ___ ___
Check:
Ex 3: x – 9 < -42
-11x – 9 < -42
Let’s use x = 4
-11(4) – 9 < -42
-11x < -33
-44 – 9 < -42
What do we do with the symbol when we divide or multiply by a negative?
___ ___
-53 < TRUE!
x > 3 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

9. Homework: P. 156 #3