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:
- We began with \( 13(6x - 9) = -33 \).
- After distributing we got \( 78x - 117 = -33 \).
- We added 117 to both sides which led to \( 78x = 84 \).
- 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.