1. TSW#3 Solving Compound Inequalities
JH&HK

2. 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

3. 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

4. Graphing This inequality is also written as 0<x and x≤4 1. -1 1 2 31 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

5. 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

6. 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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