Question

find the missing number so that the equation has infinitely many solutions. \boxed{}x - 10 = -x - 10 - 3x

Explanation:

Step1: Combine like terms on right

Combine $-x$ and $-3x$:
$-x - 3x = -4x$, so the equation becomes $\square x - 10 = -4x - 10$

Step2: Match coefficients for infinite solutions

For infinitely many solutions, the coefficients of $x$ on both sides must be equal. Set $\square = -4$ to make the equation $-4x - 10 = -4x - 10$, which is true for all $x$.

Answer:

$-4$