Let's fill in the statements and reasons step-by-step for the proof of \( x = -1 \) given the equation \( -2(x - 4) = 2x + 12 \):
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Statement (1s): \(-2(x - 4) = 2x + 12\)
Reason (1r): Given. -
Statement (2s): \(-2x + 8 = 2x + 12\)
Reason (2r): Distributive property. -
Statement (3s): \(-2x - 2x + 8 = 12\)
Reason (3r): Subtracting \(2x\) from both sides (combining like terms). -
Statement (4s): \(-4x + 8 = 12\)
Reason (4r): Combining like terms. -
Statement (5s): \(-4x = 4\)
Reason (5r): Subtracting 8 from both sides. -
Statement (6s): \(x = -1\)
Reason (6r): Division property of equality (dividing both sides by -4).
So, the proof is:
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Statement (1s): \(-2(x - 4) = 2x + 12\)
Reason (1r): Given. -
Statement (2s): \(-2x + 8 = 2x + 12\)
Reason (2r): Distributive property. -
Statement (3s): \(-4x + 8 = 12\)
Reason (3r): Adding \(2x\) to both sides (combining like terms). -
Statement (4s): \(-4x = 4\)
Reason (4r): Subtracting 8 from both sides. -
Statement (5s): \(x = -1\)
Reason (5r): Division property of equality (dividing both sides by -4).