QuestionDecember 17, 2025

Which expression is equivalent to -(1)/(4)x+(1)/(2) (1)/(4)(-x+2) (1)/(4)(-x+(1)/(2)) -(1)/(4)(x+2) -(1)/(4)(-x+(1)/(2))

Which expression is equivalent to -(1)/(4)x+(1)/(2) (1)/(4)(-x+2) (1)/(4)(-x+(1)/(2)) -(1)/(4)(x+2) -(1)/(4)(-x+(1)/(2))
Which expression is equivalent to -(1)/(4)x+(1)/(2) (1)/(4)(-x+2) (1)/(4)(-x+(1)/(2)) -(1)/(4)(x+2) -(1)/(4)(-x+(1)/(2))

Solution
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Answer

\frac{1}{4}(-x+2) Explanation 1. Distribute \frac{1}{4} in each option Expand each expression to compare with -\frac{1}{4}x + \frac{1}{2}. - Option 1: \frac{1}{4}(-x+2) = -\frac{1}{4}x + \frac{1}{2} - Option 2: \frac{1}{4}(-x+\frac{1}{2}) = -\frac{1}{4}x + \frac{1}{8} - Option 3: -\frac{1}{4}(x+2) = -\frac{1}{4}x - \frac{1}{2} - Option 4: -\frac{1}{4}(-x+\frac{1}{2}) = \frac{1}{4}x - \frac{1}{8} 2. Identify the matching expression Only Option 1 matches -\frac{1}{4}x + \frac{1}{2}.

Explanation

1. Distribute $\frac{1}{4}$ in each option<br /> Expand each expression to compare with $-\frac{1}{4}x + \frac{1}{2}$.<br /><br />- Option 1: $\frac{1}{4}(-x+2) = -\frac{1}{4}x + \frac{1}{2}$<br />- Option 2: $\frac{1}{4}(-x+\frac{1}{2}) = -\frac{1}{4}x + \frac{1}{8}$<br />- Option 3: $-\frac{1}{4}(x+2) = -\frac{1}{4}x - \frac{1}{2}$<br />- Option 4: $-\frac{1}{4}(-x+\frac{1}{2}) = \frac{1}{4}x - \frac{1}{8}$<br /><br />2. Identify the matching expression<br /> Only Option 1 matches $-\frac{1}{4}x + \frac{1}{2}$.
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