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Answer :
Final answer:
The correct arrangement is: A) the cube of the difference of 5 times x and 7 divided by the sum of 7 times x and 1: 5[(x * 5) - 7] / (7x + 1), B) 7 times the difference of 5 times x and 7 and the sum of x and 1: 7[(5x - 7) + (x + 1)], C) the sum of 5 times the cube of x, 1, and 7 times x, divided by 5: (5 * x^3 + 1 + 7x) / 5, D) the difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1: (5x^3 - 7) / (7(x + 1)).
Explanation:
To match the given verbal descriptions with their corresponding expressions, we need to analyze each verbal description and its corresponding expression carefully. Let's go through each option one by one:
A) The verbal description 'the cube of the difference of 5 times x and 7 divided by the sum of 7 times x and 1' matches with the expression: 5[(x * 5) - 7] / (7x + 1).
B) The verbal description '7 times the difference of 5 times x and 7 and the sum of x and 1' matches with the expression: 7[(5x - 7) + (x + 1)].
C) The verbal description 'the sum of 5 times the cube of x, 1, and 7 times x, divided by 5' matches with the expression: (5 * x^3 + 1 + 7x) / 5.
D) The verbal description 'the difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1' matches with the expression: (5x^3 - 7) / (7(x + 1)).
Therefore, the correct arrangement is:
A) the cube of the difference of 5 times x and 7 divided by the sum of 7 times x and 1: 5[(x * 5) - 7] / (7x + 1),
B) 7 times the difference of 5 times x and 7 and the sum of x and 1: 7[(5x - 7) + (x + 1)],
C) the sum of 5 times the cube of x, 1, and 7 times x, divided by 5: (5 * x^3 + 1 + 7x) / 5,
D) the difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1: (5x^3 - 7) / (7(x + 1)).
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