Final answer:
The expressions 6x-2(x-3) and x+3(x-2)-6 simplify to 4x+6 and 4x-6, respectively. They are not equivalent due to opposite constant terms (positive +6 vs negative -6).
Step-by-step explanation:
To show that the expressions 6x-2(x-3) and x+3(x-2)-6 are equivalent, we need to simplify both expressions.
For the first expression:
- Distribute the -2 into the parentheses: 6x - 2x + 6.
- Combine like terms: 4x + 6.
For the second expression:
- Distribute the 3 into the parentheses: x + 3x - 6.
- Subtract 6 at the end: 4x - 6.
After simplifying both expressions, we can see that they have the same terms but with different signs for the constant term. They are not equivalent because one has +6 and the other has -6.