To find which of the given equations has the solution \( x = -2 \), we can substitute \( x = -2 \) into each equation and see if they hold true.
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Equation a: \( 7 + x = 5 \) \[ 7 + (-2) = 5 \implies 5 = 5 \quad \text{(True)} \]
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Equation b: \( 3x = -12 \) \[ 3(-2) = -12 \implies -6 = -12 \quad \text{(False)} \]
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Equation c: \( -6 - x = 20 \) \[ -6 - (-2) = 20 \implies -6 + 2 = 20 \implies -4 = 20 \quad \text{(False)} \]
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Equation d: \( 8 = 3 - x \) \[ 8 = 3 - (-2) \implies 8 = 3 + 2 \implies 8 = 5 \quad \text{(False)} \]
The only equation that has the solution \( x = -2 \) is equation a: \( 7 + x = 5 \).