On our first quiz Juan scored 82. Use a compound inequality to show the possible score x he got on his second test, if the average is strictly between 74 and 80

We determine the minimum and maximum scores that Juan needs to get in order to be within the strict average range. We let x be his score.

minimum:

74 = (82 + x) / 2

The value of x from the equation is equal to 66.

maximum:

80 = (82 + x) / 2

The value of x from the equation is equal to 78.

Hence, Juan's score should fall between 66 and 78, inclusive.

Answer: 66 ≤ x ≤ 78