Question

Which two expressions are equivalent for any value of y?

Question 5 options:

3(3y + 3) and 9y + 6


9(y + 3) and 27 + 9y


9(y + 3) and 12 + 9y


3(3y + 3) and 6y + 6

Answer 1

9(y+3) and 27+9y are equivalent for any value of y

Answer 2

9(y + 3) and 27 + 9y are equivalent for any value of y

Given :

Given options

3(3y + 3) and 9y + 6

9(y + 3) and 27 + 9y

9(y + 3) and 12 + 9y

3(3y + 3) and 6y + 6  

To find:

Which two expressions are equivalent for any value of y

Sotion:  

To find equivalent equations take two expressions and equalize them as shown below

Option 1: 3(3y + 3) and 9y + 6

⇒ 3(3y + 3) = 9y + 6

⇒ 9y + 9 $\neq$ 9y + 6

∴ 3(3y + 3) and 9y + 6 are not equal for any value of y

Option 2: 9(y + 3) and 27 + 9y

⇒ 9(y + 3) = 27 + 9y

⇒ 9y + 27 = 27 + 9y

∴ 9(y + 3) and 27 + 9y are equivalent for any value of y

Option 3: 9(y + 3) and 12 + 9y

⇒ 9(y + 3) = 12 + 9y

⇒ 9y + 27 $\neq$ 12 + 9y

∴ 9(y + 3) and 12 + 9y  are not equal for any value of y

Option 4: 3(3y + 3) and 6y + 6

⇒ 3(3y + 3) = 6y + 6

⇒ 9y + 9 $\neq$ 6y + 6

∴ 3(3y + 3) and 6y + 6 are not equal for any value of y

Therefore,

From given options

9(y + 3) and 27 + 9y are equivalent for any value of y

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