To determine the property that shows the expressions \( 11 + 6x \) and \( 8x + (-2x + 6) + 5 \) are equivalent, we need to simplify the second expression.
Let's simplify \( 8x + (-2x + 6) + 5 \):
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First, distribute the negative sign in \( -2x + 6 \): \[ 8x + (-2x) + 6 + 5 \]
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Combine like terms: \[ 8x - 2x + 6 + 5 = (8x - 2x) + (6 + 5) = 6x + 11 \]
Now we have simplified \( 8x + (-2x + 6) + 5 \) down to \( 6x + 11 \).
Next, if we compare \( 11 + 6x \) with \( 6x + 11 \), we can see they are equal since addition is commutative.
Thus, the property that shows that these expressions are equivalent is the commutative property of addition, which states that changing the order of the addends does not change the sum. Specifically:
\[ 11 + 6x = 6x + 11 \]
This verifies the equivalence of the two expressions.