# compound inequality

**Definition of Compound Inequality**

- Compound Inequality is two or more simple inequalities joined by the terms 'and' or 'or'.

**Examples of Compound Inequality**

- 0 ≤
*x *≤ 4 is an example of compound inequality, which says that *x* is either 0 or 4, or any number between 0 and 4. *x *> 5 and *x* < 11="" is="" a="" compound ="" inequality,="" which="" says="" that="">*x* takes values greater than 5 and less than 11. *y* < -="" 13="" or="">*y *≥ 10 is a compound inequality, which says that the values of *y* are either less than - 13 or greater than or equal to 10.

**Solved Example on Compound Inequality**

Choose a compound inequality that represents the set of all real numbers less than or equal to - 7 or greater than or equal to 5.

**Choices:**

A. *x* ≤ - 7 or *x *> 5

B. *x* < -="" 7="" or="">*x *≥ 5

C.* x* < -="" 7="" or="">*x *> 5

D. *x* ≤ - 7 or *x *≥ 5

**Correct Answer: D**

**Solution:**

**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.

**Related Terms for Compound Inequality**