8.2 Linear Inequalities Trichotomy Property:

8.2 Linear Inequalities Trichotomy Property:

8.2 Linear Inequalities
Trichotomy Property:
The solution of an inequality is the set of all values that make the inequality
true. Two inequalities are equivalent if they have the same solution set. The
solution can be described as listed below:
Inequality
Interval
Graph
a < x < b
a ≤ x ≤ b
a ≤ x < b
a < x ≤ b
x > a
x ≥ a
x < a
x ≤ a
1
Properties of Inequalities
Addition Property
Multiplication Property
Transitive Property
Compound Sentences:
Conjunction - when first and second conditions must both be
satisfied.
Disjunction - when first or second conditions must be satisfied.
2
Examples: Solve each inequality. Express the solution in interval
notation and draw its graph on the number line.
1.
2.
3.
3
Absolute Value Inequalities
Examples: Solve each inequality. Express the solution in interval
notation and draw its graph on the number line.
4.
5.
4
Linear Inequalities (in 2 variables)
Example 6: Graph the following inequality in the coordinate plane.
Example 7: Graph the following inequality in the coordinate plane.
5
Absolute Value Inequalities:
Example 8: Solve the following inequality by graphing.
6