To find an equivalent equation, we first need to solve the given equation:
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Start with the equation: \[ x + \frac{1}{2} = -\frac{1}{4} \]
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Subtract \(\frac{1}{2}\) from both sides to isolate \(x\): \[ x = -\frac{1}{4} - \frac{1}{2} \]
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To combine the fractions on the right side, convert \(-\frac{1}{2}\) to have a common denominator of 4: \[ -\frac{1}{2} = -\frac{2}{4} \]
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Now substitute that in: \[ x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4} \]
Now we know that the solution to the equation \(x + \frac{1}{2} = -\frac{1}{4}\) is \(x = -\frac{3}{4}\).
Next, we can create equivalent equations. Here are a couple of examples:
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Adding or subtracting the same number from both sides:
- \(x + \frac{1}{2} + \frac{3}{4} = -\frac{1}{4} + \frac{3}{4}\) simplifies to \(x + \frac{5}{4} = \frac{1}{2}\).
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Multiplying or dividing both sides by the same non-zero number:
- \(2(x + \frac{1}{2}) = 2(-\frac{1}{4})\) simplifies to \(2x + 1 = -\frac{1}{2}\).
Any of these equations, or others formed in similar ways, would share the same solution \(x = -\frac{3}{4}\).
If you provide specific options, I could help identify which one of those maintains the same solution.