Question

Solve for .
(1 point)
x
5 = 2x − 11
x = −3
x = 8
x = 3
x = −8

Answer 1

To solve the equation \( \frac{x}{5} = 2x - 11 \), we can begin by eliminating the fraction. We can do this by multiplying both sides by 5:

\[
x = 5(2x - 11)
\]

Distributing the 5 on the right side:

\[
x = 10x - 55
\]

Next, we want to get all terms involving \( x \) on one side of the equation. Subtract \( 10x \) from both sides:

\[
x - 10x = -55
\]

This simplifies to:

\[
-9x = -55
\]

Now, divide both sides by -9:

\[
x = \frac{-55}{-9} = \frac{55}{9}
\]

Since \( \frac{55}{9} \) is not one of the options given in the question, it seems necessary to confirm if there is a mistake or if any of the provided values might satisfy the original equation.

Let's double-check each option against the original equation:

1. **For \( x = -3 \)**:
\[
\frac{-3}{5} = 2(-3) - 11 \implies -0.6 = -6 - 11 \implies -0.6 = -17 \quad (\text{False})
\]

2. **For \( x = 8 \)**:
\[
\frac{8}{5} = 2(8) - 11 \implies 1.6 = 16 - 11 \implies 1.6 = 5 \quad (\text{False})
\]

3. **For \( x = 3 \)**:
\[
\frac{3}{5} = 2(3) - 11 \implies 0.6 = 6 - 11 \implies 0.6 = -5 \quad (\text{False})
\]

4. **For \( x = -8 \)**:
\[
\frac{-8}{5} = 2(-8) - 11 \implies -1.6 = -16 - 11 \implies -1.6 = -27 \quad (\text{False})
\]

None of the given options are valid solutions to the equation. The correct solution is \( x = \frac{55}{9} \), which is approximately \( 6.11 \).

Therefore, if asked to choose among the provided answers, ensure that the options represent correct solutions. The correct solution \(\frac{55}{9}\) is likely just not one of the options provided in your question.