Astudent scored 83 and 91 on her first two quizzes. write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive

Let x be the score of the 3rd quiz,, then the average score will be:
(83+91+x)/3, which = (174+x)/3. but this average should be greater or equal to 85 and smaller or equal to 90:

85 ≤ (174+x)/3 ≤ 90
1st multiply all terms with 3 → 255 ≤(174+x) ≤ 270
2nd subtract 173 from all terms → 255-174 ≤174-174+x ≤270-174
81 ≤ x ≤ 96

The variables should add up to equal 1