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Using the Commutative Property, fill in the blanks to prove the two algebraic expressions are equivalent.(1 point)

y+
+x+7=4+
+7+x

1 answer

To prove that the two expressions \( y + x + 7 \) and \( 4 + y + 7 + x \) are equivalent using the Commutative Property, you can rearrange the terms as follows:

  1. Start with the left-hand side: \[ y + x + 7 \]

  2. By the Commutative Property of Addition, we can rearrange the terms in any order. So, we can rewrite it as: \[ x + y + 7 \]

  3. Now let's work with the right-hand side: \[ 4 + y + 7 + x \]

  4. Apply the Commutative Property again to rearrange this expression: \[ y + 7 + x + 4 \]

  5. Further reorder it to show that it is equal: \[ x + y + 7 + 4 \]

Thus, both sides can be expressed with the same terms, demonstrating that: \[ y + x + 7 = 4 + y + 7 + x \]

To fill in the blanks, the expression can be filled out as: \[ y + \text{(4)} + x + 7 = 4 + \text{(y)} + 7 + x \]

So the filled expression looks like: \[ y + 4 + x + 7 = 4 + y + 7 + x \]