Key Objectives • Identify solutions of inequalities. • Write, solve, and graph inequalities. • Write inequalities from graphs. Key Terms • An inequality is a mathematical statement that shows the relationship between quantities that are not equivalent using one of the following signs: • < (less than), • > (greater than), • ≤ (less than or equal to), • ≥ (greater than or equal to), or • ≠ (not equal to). • A solution of an inequality is any value that satisfies the inequality statement. Example 1 Identifying Solutions of Inequalities In Example 1, Prof. Burger describes the solutions of an inequality, which are the values of the variable that make the inequality true. 3.1.1 Graphing and Writing Inequalities
Example 2 Graphing Inequalities An inequality like 2 + x > 7 has too many solutions to list (all numbers greater than 5), so show all the solutions by graphing them on a number line. Solutions of an inequality are indicated on a number line by shading the corresponding part of the number line with an arrow indicating that the solutions continue past those shown on the graph. To show that an endpoint is a solution, draw a solid circle at that number on the number line. To show that an endpoint is not a solution, draw an empty circle at that number on the number line. This process for graphing an inequality on a number line (shading the part of the number line that corresponds to its solutions and drawing an empty or solid circle at the endpoint) is demonstrated by Prof. Burger in Example 2.
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