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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

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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.

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Examples: Solve each inequality. Express the solution in interval notation and draw its graph on the number line.

1.

2. 3.

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Absolute Value Inequalities

Examples: Solve each inequality. Express the solution in interval notation and draw its graph on the number line.

4. 5.

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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.

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Absolute Value Inequalities:

Example 8: Solve the following inequality by graphing.