On the past two tests, a student scored a 75 and 83. Write and solve a compound inequality to

find the possible values for the 3rd test score that would give him an average between 85 and 90,
inclusive.
Please give me a step by step explanation so I can learn how to solve other questions like this. Thank you have a great day :)

1 answer

85 </= (75 + 83 + x)/3 </= 90
85 </= (158 + x)/3 </= 90
so lower limit is
85*3 = 158+x
x = 97
upper is
90*3 = 158 + x
x = 112
so
97 </= x </= 112
if greater than 100 is not possible, stop at 100