Solve for x.

Question

13(6x−9)=−33

(1 point)
Responses

x = -30

x = -15

x = -22

x = -19

Answer 1

To solve the equation \( 13(6x - 9) = -33 \), we first distribute the 13:

\[ 13 \times 6x - 13 \times 9 = -33 \]

This simplifies to:

\[ 78x - 117 = -33 \]

Next, we add 117 to both sides of the equation:

\[ 78x - 117 + 117 = -33 + 117 \]

This simplifies to:

\[ 78x = 84 \]

Now, we divide both sides by 78 to solve for \( x \):

\[ x = \frac{84}{78} \]

We can simplify \( \frac{84}{78} \):

\[ x = \frac{42}{39} = \frac{14}{13} \]

None of the provided responses match that solution, indicating a possible error in the options or question setup.

Let's double-check the calculation:

1. We began with \( 13(6x - 9) = -33 \).
2. After distributing we got \( 78x - 117 = -33 \).
3. We added 117 to both sides which led to \( 78x = 84 \).
4. Dividing gives \( x = \frac{84}{78} \), which simplifies to \( x = \frac{14}{13} \).

Can you confirm the correctness of options provided? The solution of \( x = \frac{14}{13} \) does not match any of the options.