Problem 53 - Introductory Algebra for College Students

Question

What does a solid line mean in the graph of an inequality?

Step-by-Step Solution

Answer

A solid line in an inequality graph represents the solutions of 'less than or equal to' or 'greater than or equal to' inequalities. It indicates that all points on the line are included in the solution of the inequality.

Step 1: Understanding Line Types

In the graph of an inequality, two types of lines are typically used: solid lines and dashed lines. However, this question is concerning solid lines. These two lines each represent a different thing.

Step 2: Interpreting Solid Lines

In the context of inequality graphs, a solid line is used to represent the solutions of 'less than or equal to' or 'greater than or equal to' inequalities. This means that all the points on the solid line are included in the valid solution set of the inequality. The notation for these types of inequalities are: \(a \leq b\) for 'a is less than or equal to b', and \(a \geq b\) for 'a is greater than or equal to b'.

Step 3: Visualizing Solutions

The solid line in the inequality graph indicates not only the boundary between solutions and non-solutions but also, it is part of the solution region. So, any point on this line will satisfy the inequality.