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**TSW#3 Solving Compound Inequalities**

JH&HK

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Vocabulary Compound Inequality: Two inequalities connected by and/or n=number Less than: x<n Greater than: x>n Less than or equal to: x≤n Greater than or equal to: x≥n

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**Solving compound Inequalities**

All real numbers are greater than 0 and less than or equal to 4 All real numbers are less than -1 or greater than 2 0<x≤4 x<-1 or x>2

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**Graphing This inequality is also written as 0<x and x≤4 1. -1 1 2 3**

1 2 3 4 5 0<x≤4 This inequality is also written as 0<x and x≤4 2. -2 -1 1 2 3 4 x<-1 or x>2

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**Revising Both Inequality Symbols**

Solve 3<-x+2≤8. Graph the solution Solution Isolate the variable x between the two inequality signs. 3<-x+2≤8 1<-x≤6 -1>x≥-6 Write original inequality Substitute 2 to each expression Multiply each expression by -1 and reverse both inequality symbols

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**Revising Both Inequality Symbols**

Graph -7 -6 -5 -4 -3 -2 -1 -1>x>-6 The solution is greater than -6 and less than or equal to -1

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