Question

Select the expressions that are equivalent to 12n -- 8. Select all that apply. An + 4 + 3 + 4 + 4n Blin + 4 + n =12 C. 6(6n 6(6n - 2) D. 4(3n 4(3n - 2) E. 4n + 22 - 12 + 8n

Answer 1

B, D, and E.

Explanation:

We have to select all the options that simplify to 12n - 8, and to do that we go through all answer choices one by one.

A, 3n + 4 + 3n + 4 + 4n

Adding the like terms (3n, 3n, and 4n) and the numbers gives

`(3n+3n+4n)+(4+4)=10n+8_{}`

10n + 8 is not equal to the original expression; therefore, this choice does not apply.

B. 11n + 4 +n - 12

Adding the like terms and numbers gives

`(11n+n)+(4-12)=12n-8`

This expression does equal 12n - 8; therefore, this choice is correct.

C. 6 (6n - 2)

Expanding the expression gives

`36n-12`

this is not equal to 8n - 12; therefore, this choice does not apply.

D. 4 (3n - 2 )

Expanding the expression gives

`12n-8`

This choice does equal 12n - 8; therefore, it is a correct choice.

E. 4n + 2^2 - 12 + 8n

Adding the numbers and like terms gives

`(4n+8n)+(2^2-12)`
`12n+(4-12)`
`12n-8`

The resulting expression does equal 12n - 8; therefore, this choice does apply.

Hence, the correct choices are B, D, and E.