Which of the following equations has a solution of −1/2 ?
x − 1/2 = 1
x − 1 = −1/2
x + 1/2 = −1
x + 1 = 1/2
To find which equation has a solution of \( -\frac{1}{2} \), we can plug this value into each equation and check if the equation balances (both sides equal):
1. For \( x - \frac{1}{2} = 1 \):
\( -\frac{1}{2} - \frac{1}{2} = 1 \)
\( -1 \neq 1 \)
The equation does not balance, so the solution \( x = -\frac{1}{2} \) is not correct for this equation.
2. For \( x - 1 = -\frac{1}{2} \):
\( -\frac{1}{2} - 1 = -\frac{1}{2} \)
\( -\frac{3}{2} \neq -\frac{1}{2} \)
The equation does not balance, so the solution \( x = -\frac{1}{2} \) is not correct for this equation.
3. For \( x + \frac{1}{2} = -1 \):
\( -\frac{1}{2} + \frac{1}{2} = -1 \)
\( 0 \neq -1 \)
The equation does not balance, so the solution \( x = -\frac{1}{2} \) is not correct for this equation.
4. For \( x + 1 = \frac{1}{2} \):
\( -\frac{1}{2} + 1 = \frac{1}{2} \)
\( \frac{1}{2} = \frac{1}{2} \)
The equation balances, so the solution \( x = -\frac{1}{2} \) is correct for this equation.
Thus, the equation that has a solution of \( -\frac{1}{2} \) is \( x + 1 = \frac{1}{2} \).