5. Solving Compound Inequalities
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Remember that more than is represented by > and less than is represented by <.
Compound Inequality: 0
Let's write our compound inequality for the given statement by making a table. Remember that more than is represented by > and less than is represented by <.
Verbal Expression | Algebraic Expression |
---|---|
A number d | d |
A number d is more than 0 | d> 0 |
A number d is less than 10 | d< 10 |
Combine the inequalities | 0< d< 10 |
To graph an and
compound inequality, we will first note the endpoints. In this case, the lesser endpoint is 0 and the greater endpoint is 10. 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 0 and less than 10. Therefore, we will shade the number line between the endpoints.