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

If n = smallest even number, then n +2 and n + 4 are the other two numbers.

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

I'll let you solve it for n.

84, 90,96

how did you know it was 2 and 4

Hi, you would know because since it has to be an even number, you have to add by 2. But you cant do 2 twice because you have to have different numbers, therefore you go to the next possible even, by adding 4 instead of 2.

a. To find the three consecutive even numbers, let's assume that the smallest even number is represented by "n". Since we are looking for three consecutive even numbers, the next two numbers would be "n + 2" and "n + 4".

To write an inequality for the sum of these three numbers, we can add them together and set a range between 84 and 96:

n + (n + 2) + (n + 4) ≥ 84 and n + (n + 2) + (n + 4) ≤ 96

Simplifying the inequality:

3n + 6 ≥ 84 and 3n + 6 ≤ 96

b. Now let's solve the inequality.

For the lower bound:
3n + 6 ≥ 84
Subtracting 6 from both sides:
3n ≥ 78
Dividing by 3:
n ≥ 26

For the upper bound:
3n + 6 ≤ 96
Subtracting 6 from both sides:
3n ≤ 90
Dividing by 3:
n ≤ 30

Therefore, the smallest even number, "n", should be greater than or equal to 26 and less than or equal to 30.