Learning how to write a compound inequality is an essential skill for expressing two restrictions on the same variable. A compound inequality combines two simpler inequalities using the words and or or, and it can represent a limited interval, a set of values outside a range, or any situation in which multiple conditions must be considered. Understanding the correct symbols, translating verbal descriptions, and choosing the appropriate connector will help you write accurate inequalities and interpret them confidently.
What Is a Compound Inequality?
A compound inequality is an inequality that contains two conditions joined by and or or. Each condition describes a restriction on a variable.
For example:
[ -4 < x < 6 ]
This compound inequality means that (x) is greater than (-4) and less than (6). It is equivalent to writing two separate inequalities:
[ x > -4 \quad \text{and} \quad x < 6 ]
Another example is:
[ x \leq 3 \quad
