Question

Which of the following equations has a solution of −1/2 ?(1 point)

x − 1/2 = 1

x − 1 = −1/2

x + 1/2 = −1

x + 1 = 1/2

Answer 1

To find which equation has a solution of \( x = -\frac{1}{2} \), we can substitute \( x \) with \( -\frac{1}{2} \) in each equation and see which equation holds true.

Checking each equation:

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

Substitute \( x \) with \( -\frac{1}{2} \):
\( -\frac{1}{2} - \frac{1}{2} = 1 \)
\( -\frac{2}{2} = 1 \)
\( -1 \neq 1 \) (This does not hold true)

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

Substitute \( x \) with \( -\frac{1}{2} \):
\( -\frac{1}{2} - 1 = -\frac{1}{2} \)
\( -\frac{1}{2} - \frac{2}{2} = -\frac{1}{2} \)
\( -\frac{3}{2} \neq -\frac{1}{2} \) (This does not hold true)

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

Substitute \( x \) with \( -\frac{1}{2} \):
\( -\frac{1}{2} + \frac{1}{2} = -1 \)
\( 0 \neq -1 \) (This does not hold true)

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

Substitute \( x \) with \( -\frac{1}{2} \):
\( -\frac{1}{2} + 1 = \frac{1}{2} \)
\( \frac{1}{2} - \frac{1}{2} = \frac{1}{2} \)
\( 0 = \frac{1}{2} \) (This does not hold true either)

In none of the given equations is \( -\frac{1}{2} \) a solution according to the process we just carried out. Therefore, it seems there might be a mistake in the provided options or in the question itself. If you meant that the solution is \( x = -\frac{1}{2} \), none of the listed equations will have this solution according to my calculations.