Let's break down the steps taken to solve the equation \(5 - 3(x + 3) = 11 - 8x\) and match them with the appropriate properties you listed.
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Start with the original equation: \[ 5 - 3(x + 3) = 11 - 8x \]
- Property: None applied yet.
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Apply the Distributive Property: \[ 5 - 3x - 9 = 11 - 8x \]
- Matched Property: Distributive Property
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Combine Like Terms: \[ -3x - 4 = 11 - 8x \]
- Matched Property: Combine Like Terms
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Add \(8x\) to both sides (using the Addition Property): \[ 5x - 4 = 11 \]
- Matched Property: Addition Property of Equalities
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Add \(4\) to both sides (using the Addition Property): \[ 5x = 15 \]
- Matched Property: Addition Property of Equalities
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Divide both sides by \(5\): \[ x = 3 \]
- Matched Property: Division Property of Equalities
Here’s the summarized allocation of each step with properties:
- \(5 - 3(x + 3) = 11 - 8x\) - No property applied.
- \(5 - 3x - 9 = 11 - 8x\) - Distributive Property
- \(-3x - 4 = 11 - 8x\) - Combine Like Terms
- \(5x - 4 = 11\) - Addition Property of Equalities
- \(5x = 15\) - Addition Property of Equalities
- \(x = 3\) - Division Property of Equalities
No additional properties were needed for steps 1, and at step 4, both the addition to isolate terms and combining like terms were utilized.