Solve each inequality. Write the solution set in interval notation, and graph it. See Examples 4

step 1 We have problem number 42 in which we need to solve an inequality 60 60 plus 3 60 plus 3 less th

Solve each inequality. Write the solution set in interval...

Key Concepts

Graphical Representation on the Number Line

Graphing the solution set involves depicting the range of acceptable values on a number line. This visual representation typically shows a ray or segment, with an open circle indicating that an endpoint is not included, making it easier to understand and communicate the concept of all numbers that satisfy the inequality.

Interval Notation

Interval notation is a concise way to represent the set of all solutions of an inequality. It uses parentheses or brackets to describe which endpoints are included or excluded in the solution set, providing a clear and standardized format to express ranges of numbers.

Isolation of the Variable

The method of isolating the variable means rearranging the inequality to get the variable term alone on one side. This step is crucial for determining the range of values that satisfy the inequality and is analogous to the process used in solving linear equations, but with careful attention to the direction of the inequality.

Linear Inequalities

This concept involves solving inequalities that contain one or more variables, similar to solving linear equations but with additional rules due to the inequality sign. It requires performing arithmetic operations on both sides of the inequality while keeping the relationship valid, which might include reversing the inequality when multiplying or dividing by a negative number.

Properties of Inequalities

Understanding and applying the properties of inequalities is fundamental. This includes knowing that adding or subtracting the same number on both sides preserves the inequality, while multiplying or dividing both sides by a negative number reverses the inequality. These rules ensure that the inequality’s solution set is derived correctly.

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