04+-+Sec.+6.3B

=Compound Inequalities With Or =

By:Josh Hall,Kelcey Cevallos, Weslet
Compound inequality **: **Inequality with two x's connected with or**

To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be ("or") or an ("and"). Then, solve both inequalities and graph.

//Example 1//: Solve and graph: 3(//x// - 2) < 9 **or** 3(//x// - 2) > 15

3(//x// - 2) < 9

//x// - 2 < 3 //x// < 5

3(//x// - 2) > 15

//x// - 2 > 5 //x// > 7

//x// < 5 or //x// > 7. Graph:



= Example 3 = //x// ≤ - 7 or //x// ≥ 5


 * Step 1:** The algebraic model for the statement is //x// ≤ - 7 or //x// ≥ 5.


 * Step 2:** The graph of this compound inequality is shown below. Notice that the graph has two parts. One part lies to the left of -7. The other part lies to the right of 5.



__Solve and Graph__ Practice Problem 1:  2x+6  ≥ 20 or 3(x-1)  <6

Practice Problem 2: x<- 6 OR x> 13

Practice Problem 3: x ≤ -7 or x ≥ 4

Examples