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.

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).