Solving Inequalities
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Solving Inequalities

Prentice Hall's Online Lesson Quiz   Enter Web Code: aga–0104

Important

You know that 7 > – 2 is a true inequality.
However, if you multiply the numbers on both sides of the inequality symbol by a negative number, does it stay true?

Consider  the example:      

To maintain a truthful statement, the inequality symbol needs to be reversed.
This suggests that when you multiply each side of an inequality by a negative number, the order of the inequality must be reversed.

 
 EXAMPLE 1:



Any real number less than – 2 is a solution.


Notice the open circle around – 2 indicates that this point is not included.

Set-builder notation

The solution in the example above can be written using set-builder notation. The solution y < – 2 can be written as .  
This is read as the set of all numbers y, such that y is less than negative two.


 EXAMPLE 2:



Any real number greater than – 5 is a solution.
The solution set is written as:  


Notice the closed circle around – 5 indicates that this point is included.

Practical Applications

Your quiz grades are 73, 75, 89, and 91.  What is the lowest grade you can obtain on the last quiz and still achieve an average of at least 85?


 Let q = last quiz


You must score at least a  97 on the last quiz to maintain an 85 average for quizzes.