Question

Which of the following equations has a solution of −12
?(1 point)
Responses

x − 12 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1

x + 12 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1

x − 1 = −12
x minus 1 equals negative Start Fraction 1 over 2 End Fraction

x + 1 = 12
x plus 1 equals Start Fraction 1 over 2 End Fraction

Answer 1

To find which equation has a solution of \(-12\), we can substitute \(-12\) into each equation and see if the left-hand side equals the right-hand side.

1. **Equation:** \(x - 12 = 1\)
\[
-12 - 12 = -24 \quad (\text{not equal to } 1)
\]

2. **Equation:** \(x - \frac{1}{2} = 1\)
\[
-12 - \frac{1}{2} = -12.5 \quad (\text{not equal to } 1)
\]

3. **Equation:** \(x + 12 = -1\)
\[
-12 + 12 = 0 \quad (\text{not equal to } -1)
\]

4. **Equation:** \(x + \frac{1}{2} = -1\)
\[
-12 + \frac{1}{2} = -11.5 \quad (\text{not equal to } -1)
\]

5. **Equation:** \(x - 1 = -12\)
\[
-12 - 1 = -13 \quad (\text{not equal to } -12)
\]

6. **Equation:** \(x + 1 = 12\)
\[
-12 + 1 = -11 \quad (\text{not equal to } 12)
\]

None of the equations yield a valid solution for \(x = -12\).

Let’s correct the calculations and look for the equation that resolves to \(-12\):

1. **For** \(x - 12 = 1\)
\[
x = 1 + 12 = 13
\]

2. **For** \(x - \frac{1}{2} = 1\)
\[
x = 1 + \frac{1}{2} = 1.5
\]

3. **For** \(x + 12 = -1\)
\[
x = -1 - 12 = -13 \, \text{(does not match)}
\]

4. **For** \(x + \frac{1}{2} = -1\)
\[
x = -1 - \frac{1}{2} = -1.5 \, \text{(does not match)}
\]

5. **For** \(x - 1 = -12\)
\[
x = -12 + 1 = -11 \, \text{(does not match)}
\]

6. **For** \(x + 1 = 12\)
\[
x = 12 - 1 = 11 \, \text{(does not match)}
\]

There seems to be mixed results. It appears the intended choice is x-1=-12 which gives:

**Correct Option**: **x - 1 = -12** gives the result -12. Therefore the equations with \( -12 \) would possibly be incorrect in structure. Errors may be present in framing the equation options. I apologize for the confusion. The actual computations indicate that a reevaluation is required due to wrong coefficient placements or option types. Based on existing solutions, none correctly yield x=-12 correctly, please share options if discrepancies persist.