In your us history class, you have scores of 78, 89, 87 and 96 on the first four tests. to get a b, the average of the five tests must be greater than or equal to 80 and less than 90. solve an inequality to find the range of the scores needed on the fifth test to get a b

Well, since it is asking for an average, we have to add
78+89+87+96=
350... then we divide by 4
which would be 87.5 which IS greater than 80 :)
and less than 90 :)

Let x be the score of the fifth test. 

a) let's find the value of x so that to get 80. To that end use the average notion:
(78+89+87+96+x)/5 = 80
(350 + x)/5 = 80. Cross multiplication
350+x = 400  and x = 50

b) let's find the value of x so that to get 90. To that end use the average notion:
(78+89+87+96+x)/5 = 90
(350 + x)/5 = 0. Cross multiplication
350+x = 450  and x = 100

Then the value of x should be:

50 < x < 100