To solve the equation \(-7x - 12 = __ x + 12\), we can isolate the variable \(x\) on both sides.
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Let's move \(-12\) to the right side:
\[-7x = __ x + 12 + 12\]
This simplifies to:
\[-7x = __ x + 24\]
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Now, we need to find the missing coefficient. For the left side to equal the right side, we can equate the coefficients of \(x\).
\[-7x = __ x\]
This tells us that the missing coefficient must be \(-7\).
So the completed equation is:
\(-7x - 12 = -7x + 12\)
Thus, the missing number is \(-7\).