please help me to find the least possible consecutive odd integers such as that eight times the smaller one is at least 25 more than the difference of the two integers. I don't remember my teacher teaching this so please help me.

8n>n+2-n+25

n>27/8
so the smallest odd integer is 5, the next 7
check:
8*5>7-5+25
40>27 checks.

the two numbers are x and x+2. So, you know that

8x >= 25+2
8x >= 27
x >= 27/8 = 3.375
so, you need x >= 4
But x is odd, so x=5
8*5 = 40 >= 27
The previous odd integer is 3, and 8*3 < 27

To find the least possible consecutive odd integers that satisfy the given condition, let's break down the problem into steps:

Step 1: Define the variables
Let's assume the smaller odd integer as "x." Since the problem asks for consecutive odd integers, the next odd integer would be "x + 2."

Step 2: Formulate the equation
According to the problem, eight times the smaller integer (8x) should be at least 25 more than the difference between the two integers (x + 2 - x). We can now write the equation as:
8x ≥ 25 + (x + 2 - x)

Step 3: Simplify and solve the equation
Simplifying the equation, we have:
8x ≥ 25 + 2
8x ≥ 27

Now, dividing both sides of the equation by 8:
x ≥ 27/8

The smallest odd integer greater than or equal to 27/8 is 4. So, the smallest possible value for x is 4.

Step 4: Find the consecutive odd integers
Substituting x = 4 into our assumptions, we find the two consecutive odd integers as:
- Smaller integer (x): 4
- Next odd integer (x + 2): 4 + 2 = 6

Therefore, the two consecutive odd integers that satisfy the given condition are 4 and 6.

Final Answer: The least possible consecutive odd integers such that eight times the smaller one is at least 25 more than the difference of the two integers are 4 and 6.

To find the least possible consecutive odd integers, we need to follow a systematic approach to solve this problem.

Let's start by assigning variables and translating the given information into an equation:

Let's assume the smaller odd integer as "x". Since the integers are consecutive, the next odd integer will be "x + 2".

According to the given problem, eight times the smaller integer is at least 25 more than the difference of the two integers. Mathematically, this can be represented as:

8 * x ≥ (x + 2) - x + 25

Now, let's simplify and solve this equation step-by-step:

8x ≥ 2 + 25
8x ≥ 27

To find the least possible value of x, we need to divide both sides of the equation by 8:

x ≥ 27/8

Since x represents an odd integer, the next greater odd integer after 27/8 is 5. Therefore, we can choose x = 5.

Now, substitute the value of x back into the equation:

8 * 5 ≥ (5 + 2) - 5 + 25
40 ≥ 7 + 25
40 ≥ 32

The equation holds true, so the smallest possible consecutive odd integers satisfying the given condition are 5 and 7.

In conclusion, the least possible consecutive odd integers such that eight times the smaller one is at least 25 more than the difference of the two integers are 5 and 7.