Final answer:
To have infinitely many solutions in an equation, the equation needs to represent parallel lines. In this case, any real number can be the missing number.
Step-by-step explanation:
To solve the equation 2(-2x - 5) = x - 10 and find the missing number that will result in infinitely many solutions, we first simplify the equation. Distribute 2 to -2x and -5, which gives -4x - 10 = x - 10. Next, we can move all the variables to one side by subtracting x from both sides, resulting in -4x - x = -10 + 10. Simplifying further, we have -5x = 0.
To have infinitely many solutions, the equation needs to represent parallel lines. In this case, since -5x = 0 is the equation of a vertical line, any value of x will satisfy the equation, yielding infinitely many solutions. Therefore, the missing number is any real number.
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