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

Question

?(1 point)
Responses

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

−2x=211
negative 2 x equals Start Fraction 2 over 11 End Fraction

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

12x=−11

Answer 1

To find which equation has a solution of \( -\frac{11}{4} \), we can substitute \( x = -\frac{11}{4} \) into each equation and see if it holds true.

1. Equation: \(-2x = \frac{11}{2}\)
   Substitute \( x = -\frac{11}{4} \):
   \[ -2\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{22}{4} = \frac{11}{2} \implies \frac{11}{2} = \frac{11}{2} \text{ (True)} \]

2. Equation: \(-2x = \frac{2}{11}\)
   Substitute \( x = -\frac{11}{4} \):
   \[ -2\left(-\frac{11}{4}\right) = \frac{2}{11} \implies \frac{22}{4} = \frac{2}{11} \implies \frac{11}{2} \neq \frac{2}{11} \text{ (False)} \]

3. Equation: \(-\frac{1}{2}x = \frac{11}{2}\)
   Substitute \( x = -\frac{11}{4} \):
   \[ -\frac{1}{2}\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{11}{8} \neq \frac{11}{2} \text{ (False)} \]

4. Equation: \(12x = -11\)
   Substitute \( x = -\frac{11}{4} \):
   \[ 12\left(-\frac{11}{4}\right) = -11 \implies -\frac{132}{4} = -11 \implies -33 = -11 \text{ (False)} \]

Only the first equation has \( -\frac{11}{4} \) as a solution.

Therefore, the correct response is:
−2x=112 (negative 2 x equals Start Fraction 11 over 2 End Fraction)