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

Name Date

WORKSHEET 4.2: GRAPHING CONJUNCTIONS

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Two inequalities joined by the word ‘‘and’’ form a conjunction. A conjunction is true when

both of the sentences are true. Every conjunction with one variable can be graphed on a

number line.

EXAMPLES

aandbare real numbers,a<b.

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a≤x≤bincludesa,b, and the numbers between them.

----------------------------------------------------------------------------------ab

a<x≤bincludesband the numbers betweenaandb.

----------------------------------------------------------------------------------ab

a≤x<bincludesaand the numbers betweenaandb.

----------------------------------------------------------------------------------ab

a<x<bincludes the numbers betweenaandb.

----------------------------------------------------------------------------------ab

DIRECTIONS: Graph each conjunction on a number line.

1. 0 <x≤ 5 2. 2 ≤x< 5 3. − 3 <x< 0


2. x≤−4andx≥− 5 5. x>3andx≤ 4 6. x≥−1andx< 2


3. x<1andx>− 1 8. 3 >xandx≥ 0 9. − 2 <xandx< 0

CHALLENGE:Use this graph to write an inequality. − 31

141

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