To determine which equation has a solution of \( x = -8 \), we can substitute \(-8\) into each equation and see if it holds true.
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\( x - 4 = -12 \) \[ -8 - 4 = -12 \quad \text{(True)} \]
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\( x + 3 = -11 \) \[ -8 + 3 = -5 \quad \text{(False)} \]
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\( x - 10 = 2 \) \[ -8 - 10 = -18 \quad \text{(False)} \]
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\( x - 8 = 0 \) \[ -8 - 8 = -16 \quad \text{(False)} \]
The only equation that holds true with a solution of \( x = -8 \) is:
\( x - 4 = -12 \).