Final answer:
To find the number that gives the same result when multiplied by 4 or when multiplied by 7 and then added 9, we solve the equation 4x = 7x + 9, yielding x = -3.
Step-by-step explanation:
The student is asking to find a number that when multiplied by 4 gives the same result as when the number is multiplied by 7 and then have 9 added to the result. This can be represented by the equation 4x = 7x + 9. To solve for x, follow these steps:
Subtract 7x from both sides: 4x - 7x = 9.
Simplify by combining like terms: -3x = 9.
Divide both sides by -3: x = -3.
The number we are looking for is -3.