Solving Combined Inequalities Chapter 3 Section 3.4

Objective Students will find the solution sets of combined inequalities

Concept 2 inequalities put together with either the word and or the word or.

Concept A conjunction is formed by joining sentences by using the word and. Example: -2 < x and x < 3 or -2 < x < 3

Concept To solve a conjunction of two open sentences in a given variable, you find the values of the variable for which both sentences are true. The graph of a conjunction consists of the points in common between both sentences Towards middle

Concept A disjunction is formed by joining sentences by using the word or. Example: x > -3 or x < -3

Concept To solve a disjunction of two open sentences, you find the values of the variable for which at least one of the sentences is true. The graph consists of all points that are in the graph of both sentences. Towards outside

< or > open circle < or > closed circle Concept < or > open circle < or > closed circle

Concept Remember that any time you multiply or divide by a negative number you still must change the direction of your inequality sign.

Example -3 < x – 2 < 4

Example -2 < x + 1 < 4

Example 2x – 1 < 3 or 3x > x + 10

Example 1 + 5x < -4 or 4x > x + 9

Questions

Assignment Worksheet