Let the two integers be $x$ (the smaller integer) and $x+2$ (the next consecutive odd integer). According to the problem:

"The sum of an integer and 7 times the next consecutive odd integer is 6."

This translates into the equation:
$x + 7(x+2) = 6$

Step 1: Simplify the equation

$x + 7x + 14 = 6$

Combine like terms: $8x + 14 = 6$

Step 2: Solve for $x$

$8x = 6 - 14$ $8x = -8$ $x = -1$

Step 3: Find the greater integer

The greater integer is: $x+2 = -1+2 = 1$

Final Answer:

The greater integer is 1.

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Would you like a detailed verification of the solution?

Related Questions:

1. What is the value of the smaller integer in this problem?
2. Can we verify the solution by substituting into the original equation?
3. How do we solve similar problems involving consecutive even integers?
4. What is the importance of correctly interpreting "next consecutive odd integer"?
5. Can we solve this problem using substitution instead of direct algebra?

Tip:

When solving problems involving consecutive integers, always write down the relationships clearly (e.g., $x+1, x+2$ for even/odd cases). This prevents errors in setup.