Which of the following equations has a solution of −11/4

?(1 point)
Responses

−1/2x=11/2
negative 1 half x is equal to 11 halves - no response given

−2x=11/2
negative 2 x is equal to 11 halves - no response given

12x=−11
1 half x is equal to negative 11 - no response given

−2x=2/11

1 answer

To determine which equation has the solution of \( x = -\frac{11}{4} \), we can substitute \(-\frac{11}{4}\) into each equation and check if it satisfies the equation.

  1. For the equation \( -\frac{1}{2}x = \frac{11}{2} \): \[ -\frac{1}{2}\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{11}{8} \neq \frac{11}{2} \quad \text{(not a solution)} \]

  2. For the equation \( -2x = \frac{11}{2} \): \[ -2\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{22}{4} = \frac{11}{2} \quad \text{(this is a valid solution)} \]

  3. For the equation \( 12x = -11 \): \[ 12\left(-\frac{11}{4}\right) = -11 \implies -\frac{132}{4} = -11 \quad \text{(this is a valid solution)} \]

  4. For the equation \( -2x = \frac{2}{11} \): \[ -2\left(-\frac{11}{4}\right) = \frac{2}{11} \implies \frac{22}{4} = \frac{2}{11} \quad \text{(not a solution)} \]

Thus, the equations that have \( x = -\frac{11}{4} \) as a solution are:

  • \( -2x = \frac{11}{2} \)
  • \( 12x = -11 \)

If you can only select one, it seems more directly apparent that the second equation, \( -2x = \frac{11}{2} \), is the clearest match to the provided negative fraction solution.