Solving Compound Inequalities “and” & “or” Algebra 1 Section 6-4

Intersection vs. Union A compound inequality containing and is true only if both inequalities are true … in other words, where the graphs overlap. (that’s an intersection) Life example: Stand up if you are wearing black and have blond hair. So… who can stand up?

Union  “OR”  both graphs A compound inequality containing or is true if one or both of the inequalities is true … in other words it’s both of the graphs combined (that’s a union). Life example: Stand up if you are wearing black OR have blond hair. So… who can stand up?

There are two ways to write an “and” problem a) y > 5 and y < 12 (using the word “and”) b) 7 < m + 2 < 11 (one double-inequality equation) * you might want to rewrite the inequality as two separate inequalities before solving: 7 < m + 2 and m + 2 < 11

“and” questions could be phrased like this: a) Graph the solution set of y > 5 and y < 12 b) Solve and then graph the solution set of 7 < m + 2 < 11 * you might want to rewrite the inequality as two separate inequalities before solving: 7 < m + 2 and m + 2 < 11 5 12

7 < m + 2 < 11 5 < m < 9  m > 5 AND m < 9 5 9 Your answer for an “and” equation will always look like a bar-bell graph.

There is only one way to write an “or” problem Graph the solution set of x < -1 or x > 5 In an “OR” graph, you will usually have two rays going in opposite directions. -1 5

But NOT always … k < 8 or k < -2 Example: Solve and graph Sometimes the graph will NOT have two rays going in opposite directions: Example: Solve and graph 4k < 32 or -9k > 18 k < 8 or k < -2 -2 8

Another “OR” example Maybe the solution you need to graph is: x > -2 or x < 3 -2 3