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:

Let n = 1st number

n+2   2nd  even number

n+4 = 3rd even number

The sum of these 3 numbers is

n+n+2+n+4

It must be between 84 and 96  (it does not include this 84 and 96)

84< n+n+2+n+4 < 96

Now we need to solve this

Combine like terms

84 < 3n +6< 96

Subtract 6 from all sides

84 -6 < 3n+6-6 < 96 -6

78 < 3n < 90

Divide all sides by 3

78/3 < 3n/3 < 90/3

26 < n< 30