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.

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UpStudy AI · Accepted Answer

Calculate the limit $$ \lim_{x \rightarrow -6} (5x+6) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow -6}\left(5x+6\right)$$
- step1: Rewrite the expression:
  $$\lim _{x\rightarrow -6}\left(5x\right)+\lim _{x\rightarrow -6}\left(6\right)$$
- step2: Calculate:
  $$-30+6$$
- step3: Calculate:
  $$-24$$
The limit of $$5x+6$$ as $$x$$ approaches -6 is -24.

Therefore, the correct expression after applying the limit properties is:

$$ \lim_{x \rightarrow -6}(5x+6) = -24 $$

So, the correct choice is:

A. $$ \lim_{x \rightarrow -6}(5x+6) = -24 $$
The limit is -24.

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