You can represent an odd integer with the expression 2n +1, where n is any integer. Write and solve an equation to find three consecutive odd integers that have a sum of 63.

We are asked to find three consecutive odd integers that have a sum of 63. 

We can represent the three consecutive odd integers as:
- The first odd integer: \( 2n + 1 \)
- The second odd integer: \( 2n + 3 \)
- The third odd integer: \( 2n + 5 \)

Now, let's set up an equation where the sum of these three integers equals 63:

\[
(2n + 1) + (2n + 3) + (2n + 5) = 63
\]

### Step 1: Simplify the equation
Combine like terms:

\[
2n + 2n + 2n + 1 + 3 + 5 = 63
\]

\[
6n + 9 = 63
\]

### Step 2: Solve for \( n \)
Subtract 9 from both sides:

\[
6n = 63 - 9
\]

\[
6n = 54
\]

Now divide by 6:

\[
n = \frac{54}{6} = 9
\]

### Step 3: Find the three consecutive odd integers
Now that we have \( n = 9 \), substitute it back into the expressions for the three integers:
- First integer: \( 2(9) + 1 = 18 + 1 = 19 \)
- Second integer: \( 2(9) + 3 = 18 + 3 = 21 \)
- Third integer: \( 2(9) + 5 = 18 + 5 = 23 \)

### Conclusion:
The three consecutive odd integers are 19, 21, and 23.

To verify, their sum is:

\[
19 + 21 + 23 = 63
\]

Thus, the solution is correct.

Would you like any further clarification or details?

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Here are 5 related questions:
1. How would the equation change if the sum were 75 instead of 63?
2. What happens if we want

Solve for three consecutive odd integers whose sum is 63. This algebra problem explores linear equations and properties of odd numbers. Detailed steps show how to set up and solve the equation, perfect for students in Grades 6-8.

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