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# Compound Inequalitie

### Module 8

3x+1≤-11 and 3x≤0 When you see the word and you know that you will be looking for the intersection. Simplifying these compound inequalities is the first step. x≤-4 and x≤0 Solution is (-∞,-4]
x+7≥7 and x+5≤4 Simplified x≥0 and x≤-1 This question has no solution
-4x≤-12 or 3x-25≥-10 Notice the compound inequality has the word OR in it. This means the answer will be the union of the solution sets. Also notice when dividing by a negative the inequality sign will flip. Simplified x≥3 or x≥5 Solution is [3,∞)
x<-8 or x>-5 Solution (-∞,-8) or (-5,∞)
-12<3x-12≤7 Simplify 0<x≤19/3 Solution (0,19/3]
5x≤-25 and x≤0 Notice that the the word and separates the two Simplified x≤-5 and x≤0 Solution (-∞,-5]
The intersection of two sets, A and B, is the set of all elements common to both sets. A intersect B is denoted by A n B Example: A=(x is an even number greater than 0 and less than 10) B=(3,4,5,6) The intersection of the sets is (4,6)
The union of two sets, A and B, is the set of elements that belong to either of the sets. A union B is denoted by A U B Example: A=(x is an even number greater than 0 and less tham 10) B=(3,4,5,6) The Union is (2,3,4,5,6,8)
Are you looking for the Intersection or the union in this set 12x<-4 or 5x-17>-15 Union, Notice that or seperates the two sets
Are you looking for the Intersection or the union in this set x≤0 and x≥-2 Intersection, Notice that the word and seperates the two sets
Created by: danieldombrowski