Final answer:
To find the missing number so that the equation has infinitely many solutions, we set up the equation and solve for x. The missing number in this case is 0.
Step-by-step explanation:
To find the missing number so that the equation has infinitely many solutions,
we need to set up the equation so that it simplifies to an identity, where both sides of the equation are equal for all values of x.
In this case, the equation is x - 17 = -2x - 17.
To solve for x, we can add 2x to both sides of the equation to get 3x - 17 = -17.
Next, we add 17 to both sides of the equation to get 3x = 0.
Finally, divide both sides of the equation by 3 to get x = 0.
Therefore, the missing number is 0 and the equation x - 17 = -2x - 17 has infinitely many solutions.