Question

Which of the following equations has a solution of −11/4 ?(1 point)
Responses

−12x=112
negative Start Fraction 1 over 2 End Fraction x equals Start Fraction 11 over 2 End Fraction

−2x=112
negative 2 x equals Start Fraction 11 over 2 End Fraction

12x=−11
Start Fraction 1 over 2 End Fraction x equals negative 11

−2x=211

Answer 1

To determine which of the equations has a solution of \(-\frac{11}{4}\), we can substitute \(-\frac{11}{4}\) into each of the equations and check if the left-hand side equals the right-hand side.

1. **Equation: \(-12x = 112\)**
Substituting \(x = -\frac{11}{4}\):
\(-12(-\frac{11}{4}) = 12 \cdot \frac{11}{4} = \frac{132}{4} = 33\)
(No, the left side is not equal to 112)

2. **Equation: \(-\frac{1}{2}x = \frac{11}{2}\)**
Substituting \(x = -\frac{11}{4}\):
\(-\frac{1}{2}(-\frac{11}{4}) = \frac{11}{8}\)
(No, the left side is not equal to \(\frac{11}{2}\))

3. **Equation: \(-2x = 112\)**
Substituting \(x = -\frac{11}{4}\):
\(-2(-\frac{11}{4}) = \frac{22}{4} = \frac{11}{2}\)
(No, the left side is not equal to 112)

4. **Equation: \(\frac{1}{2}x = -11\)**
Substituting \(x = -\frac{11}{4}\):
\(\frac{1}{2}(-\frac{11}{4}) = -\frac{11}{8}\)
(No, the left side is not equal to -11)

5. **Equation: \(-2x = 211\)**
Substituting \(x = -\frac{11}{4}\):
\(-2(-\frac{11}{4}) = \frac{22}{4} = \frac{11}{2}\)
(No, the left side is not equal to 211)

None of the equations provided yield a solution of \(-\frac{11}{4}\). Therefore, none of the equations listed has a solution of \(-\frac{11}{4}\).