The correct equivalent expression for (k + 1)(4) is 5(4) - 6 + 5(4) - 6. It accurately reflects adding 1 to k(x) and then multiplying by 4, resulting in 8.
Option d is the correct choice.
Let's break it down:
* (k + 1)(4): This expression takes the function k(x) (5x - 6) and adds 1 to it before multiplying by 4.
* 5(4+4) - 6: This expands the parentheses (4 + 4 = 8), multiplies by 5, and then subtracts 6. However, this doesn't involve adding 1 to k(x) first.
* 5(5(4) - 6) - 6: This multiplies 5 by (5(4) - 6) = 14, but then subtracts 6 twice, which is different from adding 1 and then multiplying by 4.
* 54 - 6 + 54 - 6: This simply combines two instances of 54 - 6, but it doesn't involve k(x) or its manipulation.
Therefore, only option d) 5(4) - 6 + 5(4) - 6 accurately reflects adding 1 to k(x) and then multiplying by 4:
- 5(4) - 6 = 20 - 6 = 14 (equivalent to 5k(x) - 6)
- 14 - 6 = 8 (equivalent to adding 1 and then multiplying by 4)
So, 5(4) - 6 + 5(4) - 6 is the correct answer.