To solve this problem, we'll break it down into smaller steps:
Let's assume the number we're looking for is represented by "x".
"The product of 9 and a number increased by 7 is 126" can be translated into the equation: 9 * (x + 7) = 126
To solve for "x", we'll start by simplifying the equation: 9x + 63 = 126
Next, we'll isolate the "x" term by subtracting 63 from both sides of the equation: 9x = 126 - 63 9x = 63
Finally, we'll solve for "x" by dividing both sides of the equation by 9: x = 63 / 9 x = 7
Therefore, the number we're looking for is 7.