Question

Which of the following equations has a solution of −1/2 ?(1 point) Responses x + 1 = 1/2 x plus 1 equals Start Fraction 1 over 2 End Fraction x − 1 = −1/2 x minus 1 equals negative Start Fraction 1 over 2 End Fraction x − 12 = 1 x minus Start Fraction 1 over 2 End Fraction equals 1 x + 12 = −1

Answer 1

To determine which of the given equations has a solution of \(-\frac{1}{2}\), we can substitute \(-\frac{1}{2}\) into each equation and check if the left side equals the right side.

1. **Equation:** \(x + 1 = \frac{1}{2}\)

Substitute \(x = -\frac{1}{2}\):

\[
-\frac{1}{2} + 1 = \frac{1}{2}
\]

\[
\frac{1}{2} = \frac{1}{2} \quad \text{(True)}
\]

2. **Equation:** \(x - 1 = -\frac{1}{2}\)

Substitute \(x = -\frac{1}{2}\):

\[
-\frac{1}{2} - 1 = -\frac{1}{2}
\]

\[
-\frac{3}{2} = -\frac{1}{2} \quad \text{(False)}
\]

3. **Equation:** \(x - 12 = 1\)

Substitute \(x = -\frac{1}{2}\):

\[
-\frac{1}{2} - 12 = 1
\]

\[
-\frac{25}{2} = 1 \quad \text{(False)}
\]

4. **Equation:** \(x - \frac{1}{2} = 1\)

Substitute \(x = -\frac{1}{2}\):

\[
-\frac{1}{2} - \frac{1}{2} = 1
\]

\[
-1 = 1 \quad \text{(False)}
\]

5. **Equation:** \(x + 12 = -1\)

Substitute \(x = -\frac{1}{2}\):

\[
-\frac{1}{2} + 12 = -1
\]

\[
\frac{23}{2} = -1 \quad \text{(False)}
\]

The only equation that holds true is the **first one**:

**Answer:** \(x + 1 = \frac{1}{2}\) (This equation has a solution of \(-\frac{1}{2}\)).