Your test scores in one class are 82 and 86. what possible scores can you earn on your next test to have a test average between 84 and 89 inclusive ?

84 ≤ x ≤ 99   (you need between 84 and 99 points to have an average score between 84 and 89.  

Step-by-step explanation:

You want your average score to be between 84 and 89. The average score will come from the first two tests, and from the third test, which you don't know the score of yet,  we write this into an inequality like this...

Step 1:  Set up an inequality using the given information

84 ≤  (82 + 86 + x)/3 ≤ 89          the middle term represents the average score

Step 2:  Solve the inequality...

252 ≤ 82 + 86 + x ≤ 267         (multiply all 3 terms by 3 to get rid of the fraction)

   252 ≤ 168 + x ≤ 267          (simplify the middle term, 82 + 86 = 168)

         84 ≤ x ≤ 99              (subtract 168 from all 3 sides to isolate x)

                                            (252 - 168 = 84, 267 - 168 = 99)

So you need a score between 84 and 99 on the third test to have an average score between 84 and 89 on all three tests