Use the properties of inequalities to solve each inequality. Write answers using interval notati

step 1 In this problem, we're being asked to solve the given inequality. And solving inequalities is ve

Use the properties of inequalities to solve each inequality....

Key Concepts

Linear Inequalities

Linear inequalities are expressions that relate a linear function to a constant using inequality signs (such as <, ?, >, or ?). They are similar to linear equations, but instead of seeking specific equalities, the goal is to determine the range of values that satisfy the inequality condition. This type of problem typically involves isolating the variable on one side using arithmetic operations.

Properties of Inequalities

The properties of inequalities include the addition, subtraction, multiplication, and division properties that allow you to manipulate an inequality similarly to an equation. However, an important difference is that when you multiply or divide by a negative number, the direction of the inequality sign must be reversed. These properties are foundational for solving and simplifying inequalities.

Multiplication or Division by a Negative Number

When solving inequalities, if you multiply or divide both sides by a negative number, you must reverse the inequality sign. This is crucial because doing so maintains the logical correctness of the inequality. This key rule differentiates the process of solving inequalities from that of solving equations.

Interval Notation

Interval notation is a way of representing subsets of the real numbers by indicating an interval between two endpoints. It is used to concisely express the solution set of inequalities. Square brackets [ ] indicate that an endpoint is included in the interval, while parentheses ( ) indicate that an endpoint is not included.

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