Download Section 2.4: Linear Inequalities

2.4B Linear Inequalities
March 30, 2011
MATH 1010 ~ Intermediate Algebra
Chapter 2: LINEAR EQUATIONS AND
INEQUALITIES
Section 2.4: Linear Inequalities
Objectives:
✾
✾
✾
✾
Sketch the graph of inequalities on a number line.
Use properties of inequalities to solve linear inequalities.
Solve compound inequalities.
Solve application problems involving inequalities.
Sketch the solution on the number line:
-3 ≤ x< 2
0
1
2.4B Linear Inequalities
March 30, 2011
INTERVALS ON A REAL NUMBER LINE
Notation
[a,b]
(a,b)
[a,b)
(a,b]
[a,∞)
(a,∞)
(-∞,b]
(-∞,b)
(-∞,∞)
Inequality
a≤x≤b
Graph
2.4B Linear Inequalities
March 30, 2011
① EXAMPLE:
Graph each inequality.
a) -2 ≤ x < 3
-5
b) x ≥ -1 or x < -2
c) x > 1
-4
-5
-5
-3
-1
-2
-3
-4
-4
-2
-3
-2
-1
-1
1
3
2
1
0
0
2
1
0
2
3
3
5
4
5
4
4
5
2.4B Linear Inequalities
March 30, 2011
Properties of Inequalities
1. Addition and Subtraction Properites
2. Multiplication and Division Properties: Positive Quantities
3. Multiplication and Division Properties: Negative Quantities
4. Transitive Property
2.4B Linear Inequalities
March 30, 2011
SOLVING LINEAR INEQUALITIES
① EXAMPLE:
3x + 12 < x + 18
-10
-9
-8 -7 -6
-5 -4
-3 -2
-1
0
1
2
3
4
5
6
7
8
9
10
3
4
5
6
7
8
9
10
②
-7 ≤ 5x - 2 < 8
-10
-9
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
2.4B Linear Inequalities
March 30, 2011
③
-3x + 6 ≤ 2
or
-3x + 6 ≥ 7
④
-10
9 - x ≤ 3 + 2x
-9
and
-10
-9
-8 -7
-6
-5 -4
-3 -2
-1
0
1
2
3
4
5
4
5
6
6
7
8
10
9
3x - 7 ≤ -22
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
7
8
9
10