Question

Match each expression in column A with an equivalent expression from column Be prepared to explain your reasoning. Type the letter from column A in front of the expression in column B, that is equivalent.

A. (9x+ 5y) + (3x + 7y) 1. 12(x + y)
B. (9x + 5y)-(3x + 7y) 2. 12(x-y)
C. (9x+ 5y)-(3x-7y) 3. 6(х-2y)
D. 9x-7y+ 3x+ 5y 4. 9x +5y+ 3x-7y
E. 9х-7y + 3x-5у 5. 9x + 5y-3x + 7y
F. 9x-7y-3x-5y 6. 9x-3x + 5y-7y

Answer 1

By applying algebraic manipulation, we matched expression A with 1 and expression D with 4 from column B. Other expressions C, E, and F do not match the options provided, indicating an error or missing terms in the question.

Step-by-step explanation:

To solve this problem, we will be applying basic algebraic manipulation to match each expression in column A with an equivalent expression in column B.

1. A. (9x+ 5y) + (3x + 7y) simplifies to 12x + 12y, which is not directly listed in column B, but if we factor 12 out, we get 12(x + y). Therefore, the matching pair is A.1.
2. B. (9x + 5y) - (3x + 7y) simplifies to 6x - 2y. By factoring out 6, we get 6(x - y). Therefore, the matching pair is B.3.
3. C. (9x+ 5y) - (3x - 7y) simplifies to 6x + 12y, which cannot be directly matched with any of the options provided in column B.
4. D. 9x - 7y + 3x + 5y simplifies to 12x - 2y, which is not directly listed in column B, but reordering the terms gives us the expression 9x + 5y + 3x - 7y, which corresponds to D.4.
5. E. 9x - 7y + 3x - 5y simplifies to 12x - 12y, which is not directly listed in column B, and unfortunately, there are no matching expressions.
6. F. 9x - 7y - 3x - 5y simplifies to 6x - 12y which doesn't match any of the expressions in column B, suggesting a possible error or that the equivalent expression is missing.