Let's analyze the steps between the lines you provided and identify the relevant properties:
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From Line 1 to Line 2:
- Line 1: \(11(2 + 8x)\)
- Line 2: \(11(8x + 2)\)
The transformation from Line 1 to Line 2 involves rearranging the terms inside the parentheses. This applies the Commutative Property of Addition, which states that for any numbers \(a\) and \(b\), \(a + b = b + a\). Therefore, the correct justification for the step from Line 1 to Line 2 is:
- Commutative Property of Addition.
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From Line 2 to Line 3:
- Line 2: \(11(8x + 2)\)
- Line 3: \(88x + 22\)
To simplify Line 2 to Line 3, you distribute the \(11\) across the expression inside the parentheses:
- \(11(8x) + 11(2) = 88x + 22\)
This step is justified by the Distributive Property, which states that \(a(b + c) = ab + ac\). Therefore, the correct justification for the step from Line 2 to Line 3 is:
- Distributive Property.
Summary:
- From Line 1 to Line 2: Commutative Property of Addition.
- From Line 2 to Line 3: Distributive Property.
1 answer