Use $$ \lim _{x \rightarrow c} f(x)=-2 $$ and $$ \lim _{x \rightarrow c} g(x)=-7 $$ to find the limit. $$ \lim _{x \rightarrow c}[6 f(x)-4 g(x)] $$

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To find the limit $$\lim_{x \rightarrow c} [6f(x) - 4g(x)]$$, we can use the properties of limits, specifically the linearity of limits. This property states that:

$$
\lim_{x \rightarrow c} [a \cdot f(x) + b \cdot g(x)] = a \cdot \lim_{x \rightarrow c} f(x) + b \cdot \lim_{x \rightarrow c} g(x)
$$

Given:
$$
\lim_{x \rightarrow c} f(x) = -2 \quad \text{and} \quad \lim_{x \rightarrow c} g(x) = -7
$$

Applying the linearity property:
$$
\lim_{x \rightarrow c} [6f(x) - 4g(x)] = 6 \cdot \lim_{x \rightarrow c} f(x) - 4 \cdot \lim_{x \rightarrow c} g(x)
$$
$$
= 6 \cdot (-2) - 4 \cdot (-7)
$$
$$
= -12 + 28
$$
$$
= 16
$$

**Answer:** 
$$\boxed{16}$$
The limit is 16.

Use \( \lim _{x \rightarrow c} f(x)=-2 \) and \( \lim _{x \rightarrow c} g(x)=-7 \) to find the limit. \[ \lim _{x \rightarrow c}[6 f(x)-4 g(x)] \]

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