Let's identify the properties used in each step of solving the equation \( 5 - 3(x + 3) = 11 - 8x \):
Step 1: 5x = 15
This step seems to be leading to a conclusion based on earlier steps. We need to check the preceding calculations to understand how it got to \( 5x = 15 \).
Step 2: 5 - 3x - 9 = 11 - 8x
In this step, we have applied the Distributive Property to remove the parentheses in \( -3(x + 3) \) and combined the constant terms \( 5 - 9 \).
Step 3: x = 3
In this step, we simplify the equation to isolate \( x \). The property at play here is likely the Division Property of Equalities, assuming we divided both sides of the equation by a common factor for simplification.
Step 4: 5x - 4 = 11
This step appears to be a reorganization or simplification of the prior step. The property is likely the Addition Property of Equalities if we moved terms from one side to another, but also might involve combining like terms.
Step 5: -3x - 4 = 11 - 8x
In this step, it looks like terms have been moved or rearranged, which again brings us to the Subtraction Property of Equalities if we subtracted from both sides or Combine Like Terms if we are combining or simplifying further.
In summary:
- Step 2: Distributive Property
- Step 3: Division Property of Equalities
- Step 4: Likely Addition Property of Equalities / Combine Like Terms
- Step 5: Likely Subtraction Property of Equalities / Combine Like Terms
Therefore, more context on steps leading to or ensuring clarity on each would be beneficial for absolute precision in identifying properties directly.
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