Final answer:
After simplifying both expressions, we find that 6-4(3-2x) simplifies to -6 + 8x and (8x-4)-2 simplifies to 8x - 6. Due to the commutative property of addition, both expressions are indeed equivalent for any value of x.
Step-by-step explanation:
The question asks if the expressions 6-4(3-2x) and (8x-4)-2 are equivalent. To determine this, we'll simplify both expressions step-by-step.
First expression:
6 - 4(3 - 2x)
= 6 - 4 × 3 + 4 × 2x
= 6 - 12 + 8x
= -6 + 8x
Second expression:
(8x - 4) - 2
= 8x - 4 - 2
= 8x - 6
Upon simplifying, we find that the first expression becomes -6 + 8x and the second expression becomes 8x - 6. Since adding is commutative, meaning a + b = b + a, both expressions are indeed equivalent. They are just written differently, but they represent the same value for any x.
It's important to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable, which we have done here.