Interval Notation

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In this section, we review how to write the solution for a linear inequality in one variable using interval notation. Interval notation allows us to notate a specific interval or range of numeric values. Typically, we see this when solving a linear inequality in one variable. We may see a result of: x > 3. In this case, any value that is larger than 3 is a solution to that particular inequality. This is notated with interval notation as: (3, ∞). Additionally, we review how to display intervals using a number line. This process closely resembles interval notation. We use a bracket at the number to include it or a parenthesis to not include it. Some courses will use a filled-in circle for inclusion and an open circle for exclusion. We shade areas to visually represent the solutions to the inequality. Lastly, we will review how to write a solution using set-builder notation. As an example, x > 3 would be displayed in set-builder notation as:{x|x > 3}. This is read as "the set of all x, such that x is greater than 3". This essentially just tells us that x can take on any real number that is larger than 3.
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