Question

Which of the following equations has the same solution as the equation x + 1/2 = −1/4? (1 point)

Answer 1

To find an equivalent equation, we first need to solve the given equation:

1. Start with the equation:
\[
x + \frac{1}{2} = -\frac{1}{4}
\]

2. Subtract \(\frac{1}{2}\) from both sides to isolate \(x\):
\[
x = -\frac{1}{4} - \frac{1}{2}
\]

3. To combine the fractions on the right side, convert \(-\frac{1}{2}\) to have a common denominator of 4:
\[
-\frac{1}{2} = -\frac{2}{4}
\]

4. 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:

1. **Adding or subtracting the same number from both sides**:
- \(x + \frac{1}{2} + \frac{3}{4} = -\frac{1}{4} + \frac{3}{4}\) simplifies to \(x + \frac{5}{4} = \frac{1}{2}\).

2. **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.