Which of the following equations has a solution of −1/2

Question

?(1 point)
Responses

x − 1/2 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1

x + 1/2 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1

x − 1 = −1/2
x minus 1 equals negative Start Fraction 1 over 2 End Fraction

x + 1 = 1/2
x plus 1 equals Start Fraction 1 over 2 End Fraction

Answer 1

To determine which equation has a solution of \( -\frac{1}{2} \), we can substitute \( x = -\frac{1}{2} \) into each equation and see which one balances.

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

   Substitute \( x = -\frac{1}{2} \): \[ -\frac{1}{2} - \frac{1}{2} = 1 \implies -1 = 1 \quad \text{(not true)} \]

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

   Substitute \( x = -\frac{1}{2} \): \[ -\frac{1}{2} + \frac{1}{2} = -1 \implies 0 = -1 \quad \text{(not true)} \]

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

   Substitute \( x = -\frac{1}{2} \): \[ -\frac{1}{2} - 1 = -\frac{1}{2} \implies -\frac{3}{2} = -\frac{1}{2} \quad \text{(not true)} \]

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

   Substitute \( x = -\frac{1}{2} \): \[ -\frac{1}{2} + 1 = \frac{1}{2} \implies \frac{1}{2} = \frac{1}{2} \quad \text{(true)} \]

The equation that has a solution of \( -\frac{1}{2} \) is:

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