Final answer:
Martie correctly distributed the negative sign and the -3 in the expression (2-x)-3(x-4), resulting in 2 - x - 3x + 12. To complete the simplification, she should combine like terms to get -4x + 14.
Step-by-step explanation:
The student is working on simplifying an algebraic expression. The provided expression is (2-x)-3(x-4). The first step in the simplification process is to distribute the negative sign and the -3 across the terms inside the parentheses, which has been done correctly to yield 2 - x - 3x + 12. Now, we combine like terms to eliminate terms wherever possible to simplify:
- Combine the constant terms: 2 + 12 = 14.
- Combine the ‘x’ terms: -x - 3x = -4x.
The expression simplifies to -4x + 14. This is the simplest form of the expression. To verify the simplification, we can check the answer to ensure it is reasonable by substituting values for x and comparing the result with the original expression.