Which of the following equations has a solution of −12

Question

−
1
2
?(1 point)
Responses

x + 1 = 12
𝑥

+

1

=

1
2
x plus 1 equals Start Fraction 1 over 2 End Fraction

x − 12 = 1
𝑥

−

1
2

=

1
x minus Start Fraction 1 over 2 End Fraction equals 1

x − 1 = −12
𝑥

−

1

=

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

x + 12 = −1........

Answer 1

To determine which equation has a solution of \(-12 \frac{1}{2}\), we first convert \(-12 \frac{1}{2}\) to an improper fraction:

\[ -12 \frac{1}{2} = -12 - \frac{1}{2} = -\frac{24}{2} - \frac{1}{2} = -\frac{25}{2} \]

Now we will solve each equation to see which one has this solution.

1. Equation: \(x + 1 = 12\) \[ x = 12 - 1 = 11 \] Not \(-\frac{25}{2}\).

2. Equation: \(x + 1 = \frac{1}{2}\) \[ x = \frac{1}{2} - 1 = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2} \] Not \(-\frac{25}{2}\).

3. Equation: \(x - 12 = 1\) \[ x = 1 + 12 = 13 \] Not \(-\frac{25}{2}\).

4. Equation: \(x - 1 = -12\) \[ x = -12 + 1 = -11 \] Not \(-\frac{25}{2}\).

5. Equation: \(x + 12 = -1\) \[ x = -1 - 12 = -13 \] Not \(-\frac{25}{2}\).

Based on the evaluations above, none of the given equations yield a solution of \(-12 \frac{1}{2}\) or \(-\frac{25}{2}\). Please double-check the problem statement or the equations, as none of them match the specified solution.