Question

Use t = 3 and t = 7 to determine if 6t + 12 and 6(t + 2) are equivalent. Which statements are true? Check all that apply. The value of the first expression when t = 3 is not equal to the value of the second expression when t = 3. The value of the first expression when t = 7 is not equal to the value of the second expression when t = 7. The value of both expressions when t = 3 is 30. The value of both expressions when t = 7 is 54. The expressions are equivalent. The expressions are not equivalent.

Answer 1

So firstly, let's solve the expressions when t = 3 and t = 7

First expression:

`6(3)+12\\ 18+12\\ 30`

`6(7)+12\\ 42+12\\ 54`

Second expression:

`6(3+2)\\ 6(5)\\ 30`

`6(7+2)\\ 6(9)\\ 54`

Also note that if we foil the second expression, it is the same as the first expression.

So all that apply are:

- The value of both expressions when t = 3 is 30

- The value of both expressions when t = 7 is 54

- The expressions are equivalent