Question

now, we factor and cancel common factors.
\\(\lim_{x\to - 6^{-}}\frac{5x + 30}{-(x + 6)}=\lim_{x\to - 6^{-}}\frac{\square(x + 6)}{-(x + 6)}\\)
\\(=\lim_{x\to - 6^{-}}\square\\)
\\(=\square\\)

Explanation:

Step1: Factor the numerator

Factor out 5 from $5x + 30$ to get $5(x + 6)$. So, $\lim_{x
ightarrow - 6^{-}}\frac{5x + 30}{-(x + 6)}=\lim_{x
ightarrow - 6^{-}}\frac{5(x + 6)}{-(x + 6)}$.

Step2: Cancel common factors

Cancel out the common factor $(x + 6)$ (since $x
eq - 6$ when taking the limit). We get $\lim_{x
ightarrow - 6^{-}}\frac{5(x + 6)}{-(x + 6)}=\lim_{x
ightarrow - 6^{-}}- 5$.

Step3: Evaluate the limit

The limit of a constant function $y=-5$ as $x$ approaches $-6$ from the left is just the constant itself. So, $\lim_{x
ightarrow - 6^{-}}-5=-5$.

Answer:

$-5$