Find the limit if it exists. \[ \lim _{x \rightarrow-6}(5 x+6) \] Which of the following shows the correct expression after the limit properties have been applied? A. \( \lim _{x \rightarrow-6} 6 \) B. 5. \( \lim _{x \rightarrow-6} x \) C. 5. \( \lim _{x \rightarrow-6} x+\lim _{x \rightarrow-6} 6 \) D. 5. \( \lim _{x \rightarrow-6} x=\lim _{x \rightarrow-6} 6 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow-6}(5 x+6)=\square \) (Simplify your answer.) \( \square \) B. The limit does not exist.

To find the limit, we can directly substitute \( x \) with \(-6\) in the expression: \[ \lim _{x \rightarrow -6}(5x + 6) = 5(-6) + 6 = -30 + 6 = -24. \] Now, among the provided choices, we need to explore which correctly represents the expression after applying limit properties. Choice A states: \[ \lim _{x \rightarrow -6} 6 \] However, this does not reflect the original expression appropriately since we should apply the limit to \( 5x + 6 \). Choice B states: \[ \lim _{x \rightarrow -6} x \] This implies evaluating the limit solely of \( x \), which does not incorporate \( 5x + 6 \). Choice C segments \( 5 \) and shows: \[ \lim _{x \rightarrow -6} x + \lim _{x \rightarrow -6} 6, \] This could indicate evaluating "5 times the limit of \( x \)", but doesn't keep the structure of the original statement. Finally, choice D mentions: \[ 5 \cdot \lim _{x \rightarrow -6} x = \lim _{x \rightarrow -6} 6, \] which also doesn't remain true to the original expression \( 5x + 6 \). None of the choices seem to directly correspond to the limit we calculated, which is \(-24\). However, since B suggests the limit doesn't exist which is incorrect, it seems like the most straightforward simplification is the evaluation of the linear equation directly leading to our result: A. \( \lim _{x \rightarrow -6}(5x + 6) = -24 \)