Final answer:
The phrase "eight times the sum of 7x and seven" translates to the algebraic expression 8(7x + 7), which is option (a), demonstrating the use of the distributive property.
Step-by-step explanation:
The question asks to translate the word phrase "eight times the sum of 7x and seven" into an algebraic expression. Considering the rules of arithmetic operations and order of operations, the sum of 7x and seven must be calculated first before multiplying the result by eight.
The correct algebraic expression is therefore 8(7x + 7). This is because you first need to add 7x and seven together and then multiply that sum by eight. The expression aligns with the distributive property of multiplication over addition, where the eight is distributed to both terms inside the parentheses when simplified.
Step-by-step Explanation:
Identify the sum indicated by the word phrase: (7x + 7).
Multiply the entire sum by eight to represent "eight times": 8 * (7x + 7).
Check that the multiplication is applied to the entire sum to ensure the correct operation.