Final answer:
The missing number in Melissa's equation with infinitely many solutions is -3. By inserting this number, the equation on both sides simplifies to an identical expression, ensuring infinitely many solutions.
Step-by-step explanation:
The question seems to pertain to solving an algebraic equation where Melissa has found that the equation has infinitely many solutions. For an equation to have infinitely many solutions, both sides of the equation must be identical. The original equation appears to be 5(x + missing number) = 5(x+2) +5, and since the equation has infinitely many solutions, the missing number must make the equation identical on both sides after simplifying.
To determine the missing number, we can assume the equation without the missing number to be 5(x) = 5(x+2) +5. If we distribute the 5 on the left, we get 5x, and distributing the 5 on the right, we get 5x + 10 + 5, which simplifies to 5x + 15. To have infinite solutions, 5x on the left must equal 5x + 15 on the right, but that cannot happen unless the +15 does not exist. Therefore, the missing number is such that when multiplied by 5, it eliminates the +15 on the right side. If we take 'missing number' times 5 to equal -15, the 'missing number' is -3.
Thus, the missing number Melissa is looking for is -3, which, when inserted back into the equation, will result in both sides being identical and the equation having infinitely many solutions.