Three consecutive even numbers have a sum between 84 and 96. a. write an inequality to find the three numbers. let n represent the smallest even number. b. solve the inequality. a. 84 ≤ n + (n + 2) + (n + 4) ≤ 96 b. 78 ≤ n ≤ 90 a. 84 < n + (n + 2) + (n + 4) < 96 b. 26 < n < 30 a. 84 < n + (n + 1) + (n + 2) < 96 b. 27 < n < 31 a. n + (n + 2) + (n + 4) < –84 or n + (n + 2) + (n + 4) > 96 b. n < –30 or n > 31

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30

Step-by-step explanation:

Using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'.  So, the expression to represent three consecutive even numbers is:  n + (n + 2) + (n + 4).

Since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:

84 < n + (n + 2) + (n + 4) < 96

In order to solve for 'n', we must first combine like terms:

84 < 3n + 6 < 96

Subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90

Divide 3 by all sides:  78/3 < 3n/3 < 90/3 or 26 < n < 30.

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: