To find which of the given equations has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \), we first need to solve this equation.
-
Start with the original equation: \[ x + \frac{1}{2} = -\frac{1}{4} \]
-
Subtract \( \frac{1}{2} \) from both sides: \[ x = -\frac{1}{4} - \frac{1}{2} \]
-
Convert \( \frac{1}{2} \) to a fraction with a denominator of 4: \[ \frac{1}{2} = \frac{2}{4} \]
-
Now replace it in the equation: \[ x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4} \]
Now we need to check each of the other equations to see if any of them result in \( x = -\frac{3}{4} \).
1. For \( x + 1.5 = 0.75 \): \[ x = 0.75 - 1.5 = -0.75 \quad (\text{not } -\frac{3}{4}) \]
2. For \( x + \frac{1}{2} = \frac{5}{4} \): \[ x = \frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \quad (\text{not } -\frac{3}{4}) \]
3. For \( x - 0.70 = -0.05 \): \[ x = -0.05 + 0.70 = 0.65 \quad (\text{not } -\frac{3}{4}) \]
4. For \( x - \frac{1}{4} = 1 \): \[ x = 1 + \frac{1}{4} = 1.25 \quad (\text{not } -\frac{3}{4}) \]
None of the first four equations yield \( x = -\frac{3}{4} \).
After checking all of them, we realize that none matches the solution \( -\frac{3}{4} \). Since the first part was mainly about finding the solutions systematically, verify one more time.
The final original calculation:
- Adding \( \frac{1}{2} = 0.5 \) gives: \[ -\frac{1}{4} - 0.5 = -0.75 \text{ or } -\frac{3}{4}. \]
The results indicate that you might select \( x - 0.70 = -0.05 \), which leads closer to the realm of \( -0.75 \), but it’s not equivalent to \( -3/4\).
No equations provided have the same solution, hence you may check around whether more are given or validate your assumptions on the problem prompt if more context is missed.
1 answer