To complete the solution step-by-step, let's start from where you left off with the expression:
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Start with the original expression: \[ -3(-13 + m) + 11 \]
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Apply the Distributive Property: \[ -3 \cdot (-13) + (-3 \cdot m) + 11 \] Simplifying this gives: \[ 39 + (-3 \cdot m) + 11 \]
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Combine like terms using the Commutative Property of Addition: \[ 39 + 11 + (-3 \cdot m) \] Simplifying the constants: \[ 50 + (-3 \cdot m) \]
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Apply the Inverse Property of Addition (note that \(50\) can be rewritten): \[ -3 \cdot m + 50 \]
Since we were asked to show equivalence to \(-3 \cdot m + 12\), we need to consider any connections we might have missed in combining the constants. Thus:
- Note that \(39 + 11 = 50\), which does not yield \(12\) unless certain assumptions or adjustments are made in the initial problem statement.
To directly compare with \(-3(m) + 12\), we can see the focused constant change indicating corrections in either algebraic expression or adjustments based on initial operations.
Thus, the final expression shows a clear algebraic flow: \[ -3 \cdot m + 50 \]
Conclusively, we see that in this particular case, to resolve or alter \(50\) to become \(12\), an observed stake in manipulative mathematics would indicate verification of values inputted in the original equation, suggesting checks were passed initially in step \(1\) and recapped through comparative transformations.
If we adjust the addition of constants correctly, we can derive formatively toward equivalency notion within limitations set upon the original algebraic framework.
Final Representation: \[ -3(−13 + m) + 11 \equiv -3m + 50 \quad \text{(for the original values given)} \] As it stands, complete assurances enforce cluster confirmations would yield post verification—especially error checks can bridge the gap for consistency of \(m\).