Final answer:
To find the missing number so that the equation has infinitely many solutions, set the equation equal to 0 and solve for the missing number, which is 0.
Step-by-step explanation:
To find the missing number so that the equation has infinitely many solutions, we need to set the equation equal to 0 and then solve for the missing number. So, we rewrite the equation as 0 = x - 10 - 2x - 3x + 10. Combining like terms, we have 0 = -4x, which simplifies to 0 = x.
Therefore, the missing number is 0, which makes the equation x - 10 - 2x = 3x - 10 have infinitely many solutions, since any value of x will satisfy it.
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