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Determine whether the two expressions are equivalent. Explain your reasoning.

8. (n²+ 4) - n² and 4n

9. 3x + 5 and 2(x + 3)

10. 15 - 6x and 15(1 - 6x)

11. (y + y + 2 + y) + 3y and 6y + 2

12. 8y- 3 + 10y and 3(6 - 1)

User Fadli
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1 Answer

5 votes
Let us evaluate each pair of expressions one at a time.
8. (n²+4) - n² and 4n.
(n²+4) - n² = n²+ 4 - n² = 4 which is not equal to 4n.
NOT EQUIVALENT

9. 3x + 5 and 2(x + 3)
2(x + 3) = 2x + 6 which is not equal to 3x + 5.
NOT EQUIVALENT

10. 15 - 6x and 15(1 - 6x)
15(1 - 6x) = 15 - 90x which is not equal to 15 - 6x
NOT EQUVALENT

11. (y + y + 2 + y) + 3y and 6y + 2
(y +y +2 + y) + 3y = y+y+y +2 + 3y = 3y + 2 + 3y = 6y + 2.
It matches the other expression.
EQUIVALENT

12. 8y - 3 + 10y and 3(6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3
3(6 - 1) = 3(5) = 15
The two expressions do not match.
NOT EQUIVALENT.

Answer: Only the expressions in number 11 are equivalent.
User Sevenseacat
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