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 ju

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

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Key Concepts

Properties of Inequalities

This concept involves understanding that inequalities can be manipulated through operations such as addition, subtraction, multiplication, and division, much like equations. However, an important caution is required: when multiplying or dividing both sides by a negative number, the inequality sign must be reversed. These properties allow us to isolate the variable and solve the inequality in a systematic way.

Solving Linear Inequalities

Solving linear inequalities follows a process similar to that of solving linear equations. The goal is to isolate the variable on one side of the inequality while maintaining the correct relational sign. This process includes combining like terms, applying the properties of inequalities, and sometimes reversing the inequality sign, ultimately leading to a solution that specifies the set of values satisfying the inequality.

Interval Notation

Interval notation is a mathematical shorthand that expresses sets of numbers, particularly ranges of solutions to inequalities. It uses symbols like parentheses and brackets to denote whether endpoints are included or excluded from the solution set. In the context of solving inequalities, interval notation provides a clear and concise way to describe the set of all numbers that satisfy the inequality.

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