1. Solving Compound Inequalities
NOTES 1.4
Solving
Compound Inequalities

2. Graphing Inequalities
Open dot: > or < ( , )
Closed dot: ≥ or ≤ [ , ]
Which direction to shade the graph?
If x is on left, shade in the direction of arrow
If x is on the right, shade opposite the arrow

3. Solving Inequalities and Graphing
7x – 5 < 6x + 4
x – 5 < 4
x < 9 -5 9
Interval Notation
(-∞, 9)

4. Solving Inequalities and Graphing
4(x – 3) < 2(2x – 5)
4x – 12 < 4x – 10
– 12 < – 10 (true)
All real #’s
Interval Notation
(-∞, ∞)

5. Ex- special case 2 2(3x + 5) > 6(x – 1) + 17
10 > 11 (false)
NO SOLUTION
- no value of x works !

6. COMPOUND INEQUALITIES “AND” Case
13 < 2x+7
2x+7<17
13< 2x + 7< 17
x < 5
x > 3
3 < x < 5
Interval Notation
(3, 5)

7. COMPOUND INEQUALITIES “AND” Case
Interval Notation
[7, 6) -7 6

8. COMPOUND INEQUALITIES “OR” case
y – 2> -3 or y + 4 < -3
y > y < -7 -7 -5 -3 -1
Interval Notation
(- ∞,-7) and (-1,∞)

9. COMPOUND INEQUALITIES “OR” case
Interval Notation:
All real numbers

10. COMPOUND INEQUALITIES “AND” Case-7 6
Interval Notation [-7, 6)