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. Well, we solve inequalities ve

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

Key Concepts

Interval Notation

Interval notation is a method for writing subsets of the real numbers. It describes the solution set of an inequality by denoting the set’s endpoints and indicating whether they are included (using square brackets) or not (using parentheses).

Multiplication or Division by a Negative Number

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign reverses. This rule is crucial in obtaining the correct solution when handling inequalities.

Distributive Property

The distributive property is used to eliminate parentheses by multiplying the factor outside the parentheses with each term inside. This step is essential in simplifying expressions within inequalities and equations.

Properties of Inequalities

The properties of inequalities, such as adding or subtracting the same value on both sides, are key to maintaining the inequality's balance. These properties ensure that the inequality holds true throughout the solving process, except when multiplying or dividing both sides by a negative number.

Linear Inequalities

Linear inequalities involve inequalities with variables raised only to the first power. They are similar to linear equations but use inequality signs (<, >, ?, or ?) instead of an equals sign. Solving them requires similar steps as solving linear equations, while also paying attention to the direction of the inequality.

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