Question

Which of the following equations has the same solution as the equation x + 1/2 = −1/4
x + 1.5 = 0.75
x + 1/2 = 5/4
x − 0.70 = −0.05
x − 1/4 = 1

Answer 1

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.

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

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

3. Convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
\frac{1}{2} = \frac{2}{4}
\]

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.