Solve each inequality. Give the solution set using interval notation. -8 >3x-5>-12

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as '>', '<', '≥', and '≤'. Understanding how to manipulate inequalities is crucial for solving them, as the direction of the inequality can change when multiplying or dividing by negative numbers.

Compound Inequalities

A compound inequality consists of two or more inequalities that are combined into one statement. In the given question, -8 > 3x - 5 > -12 is a compound inequality that can be solved by breaking it into two separate inequalities. Solving compound inequalities requires finding the intersection of the solution sets of the individual inequalities.

Interval Notation

Interval notation is a way of representing a set of numbers between two endpoints. It uses parentheses and brackets to indicate whether the endpoints are included (closed interval) or excluded (open interval). For example, the interval (a, b) includes all numbers greater than 'a' and less than 'b', but does not include 'a' and 'b' themselves. This notation is essential for expressing the solution set of inequalities succinctly.