To determine which of the equations has a solution of \( x = -8 \), we will substitute \(-8\) into each equation and see if the equation holds true.
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For the equation \( x + 3 = -11 \): \[ -8 + 3 = -5 \quad (\text{not } -11) \]
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For the equation \( x - 10 = 2 \): \[ -8 - 10 = -18 \quad (\text{not } 2) \]
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For the equation \( x - 4 = -12 \): \[ -8 - 4 = -12 \quad (\text{this is true}) \]
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For the equation \( x - 8 = 0 \): \[ -8 - 8 = -16 \quad (\text{not } 0) \]
The equation that has a solution of \( x = -8 \) is: \( x - 4 = -12 \).