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 \(-\frac{1}{2}\)).