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

Question

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 \(-\frac{11}{4}\).