Your test scores in one class are 8484 and 88. What possible scores can you earn on your next test to have a test average between 86 and 90, inclusive
4*86 <= 84+84+88+x <= 4*90
To determine the possible scores you can earn on your next test, we need to consider the given test scores and the desired test average.
Let's denote the next test score as "x".
The average of all the test scores (including the next test score) can be calculated by summing all the scores and dividing by the total number of scores:
Average = (8484 + 88 + x) / 3
Now, we want the average to be between 86 and 90, inclusive. Therefore, we can set up the following inequality:
86 ≤ (8484 + 88 + x) / 3 ≤ 90
To solve this inequality, we can simplify the expressions and multiply all terms by 3 to get rid of the fraction:
258 ≤ 8568 + 264 + 3x ≤ 270
Combining like terms, we have:
258 ≤ 8832 + 3x ≤ 270
Next, we can subtract 8832 from all parts of the inequality:
-8574 ≤ 3x ≤ -8562
Now, divide all parts of the inequality by 3:
-2858 ≤ x ≤ -2854
So, the possible scores you can earn on your next test to have a test average between 86 and 90 (inclusive) are -2858 to -2854. Note that negative scores might not be realistic, so in a practical sense, you can consider a score of 0 to 4 as possible scores.