Solve each inequality. Graph the solution set and write the answer in a) set notation and b) int

step 1 The first thing we're being asked to do is to solve the given inequality. Remember, you solve in

Solve each inequality. Graph the solution set and write the...

Key Concepts

Interval Notation

Interval notation expresses a range of values on the real number line. It uses parentheses to indicate that an endpoint is not included and brackets to indicate inclusion, providing a concise way to represent continuous sets of numbers.

Graphing on the Number Line

Graphing the solution to an inequality on a number line provides a visual representation of all the values satisfying the inequality. This often involves drawing an open or closed circle at a critical number and shading the region extending in the direction indicated by the inequality.

Set Notation

Set notation is a method of specifying a collection of elements that satisfy a given condition. It is commonly used to express the solution set of an inequality by listing conditions on the variable inside curly brackets.

Linear Inequalities

A linear inequality is similar to a linear equation but uses inequality signs (<, >, ?, ?) instead of an equality sign. They describe a range of values rather than a specific value and are solved using many of the same algebraic steps as equations, taking care to reverse the inequality when multiplying or dividing by a negative number.

Properties of Inequality Operations

When solving inequalities, performing the same operation on both sides of the inequality maintains the relationship, except when multiplying or dividing by a negative number, which requires reversing the inequality sign. This property is crucial for correctly isolating the variable.

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