Question

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

−1/2x=11/2


−2x=11/2


1/2x=−11


−2x=2/11

Answer 1

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

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

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

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

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

From the evaluations, the second equation \(-2x = \frac{11}{2}\) is the only one that gives \(-\frac{11}{4}\) as a solution.

Thus, the correct response is:
\(-2x = \frac{11}{2}\)