The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.3: GRAPHING DISJUNCTIONS

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Two inequalities joined by the word ‘‘or’’ form a disjunction. A disjunction is true when at

least one of the sentences is true. Every disjunction with one variable can be graphed on a

number line.

EXAMPLES

aandbare real numbers,a<b.

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x≤aorx≥bincludes the numbers less than or equal toaor

the numbers greater than or equal tob. ab

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x<aorx≥bincludes the numbers less thanaor the numbers

greaterthanorequaltob. ab

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x≤aorx>bincludes the numbers less than or equal toaor

the numbers greater thanb. ab

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x<aorx>bincludes the numbers less thanaor the numbers

greater thanb. ab

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DIRECTIONS: Graph each disjunction on a number line.

1. x<1orx≥ 3 2. x≤0orx≥ 5 3. x<−1orx≥ 1


2. x<1orx> 2 5. − 1 ≥xorx≥ 3 6. 7 ≥xorx> 10


3. 0 ≥xor 3<x 8. x≥2orx≤ 1 9. x≥−1orx<− 2

CHALLENGE:Describe the graph of the inequality that models this situation:

a number larger than 10 or less than 5.

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Copyright

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.