Question

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

Answer 1

To determine which of the equations has a solution of \(-\frac{1}{2}\), we can substitute \(-\frac{1}{2}\) into each option and check if the equation holds true.

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

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

\[
-\frac{1}{2} + \frac{1}{2} = 0 \quad \text{(not equal to -1)}
\]

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

This is the same as the first equation and has already been checked.

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

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

\[
-\frac{1}{2} - \frac{1}{2} = -1 \quad \text{(not equal to 1)}
\]

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

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

\[
-\frac{1}{2} + 1 = \frac{1}{2} \quad (This is true)
\]

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

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

\[
-\frac{1}{2} - 1 = -\frac{3}{2} \quad \text{(not equal to -1/2)}
\]

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

This is similar to the previous equation and has already been checked.

The only equation that holds true when substituting \(-\frac{1}{2}\) is \(x + 1 = \frac{1}{2}\).

Thus, the equation with a solution of \(-\frac{1}{2}\) is:

\[
\boxed{x + 1 = \frac{1}{2}}
\]