5. Solving Compound Inequalities
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Remember that less than is represented by < and greater than is represented by >.
Let's write our compound inequality for the given statement by making a table. Remember that less than is represented by < and greater than is represented by >.
Verbal Expression | Algebraic Expression |
---|---|
A number p | p |
A number p is less than 6 | p< 6 |
A number p is greater than 2 | p> 2 |
Combine the inequalities | 2< p< 6 |
To graph an and
compound inequality, we will first consider the endpoints. In this case, the lesser endpoint is 2 and the greater endpoint is 6. We also know that neither of these two values are included in the solution set of the inequality, which we indicate with open circles.
The solution set lies in the area that is both greater than 2 and less than 6. Therefore, we will shade the number line between the endpoints.