Download 1.4 Solving Inequalities

1.4 Solving Inequalities
Review: Graphing Inequalities
• Open dot:
> or <
• Closed dot: > or <
• Which direction to shade the graph?
– Let the arrow point the way
Note: the variable has to be on the left for this
trick to work
Solving Inequalities and
Graphing
7x – 5 < 6x + 4
x–5<4
x<9
-5
0
9
Interval Notation
(-∞, 9)
Solving Inequalities and
Graphing
x2
x
9
9x  x  2
10x  2
1
x
5
-1
0
1
2
Interval Notation
(-∞, 1/5 ]
Solving Inequalities and
Graphing
4(x – 3) < 2(2x – 5)
4x – 12 < 4x – 10
– 12 < – 10
All reals
Interval Notation
(-∞, ∞)
Ex- special case 2
•
•
•
•
•
•
•
2(3x + 5) > 6(x – 1) + 17
6x + 10 > 6x – 6 + 17
6x + 10 > 6x – 6 + 17
6x + 10 > 6x + 11
10 > 11
NO SOLUTION
- no value of x works !
COMPOUND INEQUALITIES
“AND” Case
13< 2x + 7< 17
x<5
x>3
3<x<5
13 < 2x+7
2x+7<17
Interval Notation
(3, 5)
COMPOUND INEQUALITIES
“AND” Case
 20  3x  1  19
 20  3x  1
x  7
3x  1  19
x6
7  x  6
-7
0
6
COMPOUND INEQUALITIES
“OR” case
y – 2> -3 or y + 4 < -3
y > -1
y < -7
-7
-5
Interval Notation
(- ∞,-7) and (-1,∞)
-3
-1
COMPOUND INEQUALITIES
“OR” case
3( x  1)  4
OR
3x  3  4
3x  1
1
x
3
 2( x  3)  4
 2x  6  4
 2x  10
x  5
Interval Notation:
All real numbers