Final answer:
The equivalent expression for - 1/2 (2 - 2x) + 3 is obtained by distributing the -1/2, combining terms, and simplifying, resulting in x + 2, which is option A.
Step-by-step explanation:
The question asks which of the following expressions is equivalent to - 1/2 (2 – 2x) + 3. To find the equivalent expression, we need to simplify the given expression step by step:
- Distribute the -1/2 into the parentheses: -1/2 × 2 = -1 and -1/2 × -2x = x.
- Combine the terms: -1 + x + 3.
- Simplify by adding the constants: x + 2.
By distributing the -1/2 into the parentheses and combining the resulting terms, the expression -1/2(2 – 2x) + 3 simplifies to x + 2. Therefore, the equivalent expression is x + 2, aligning with option A. This step-by-step simplification process elucidates the transformation of the original expression into its equivalent, aiding in a clear understanding of the mathematical operations involved.
The equivalent expression is therefore x + 2, which corresponds to option A.