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Let's solve the given problem step-by-step.

### Given functions:
- \( f(x) = 2x \)
- \( g(x) = |x - 5| \)
- \( h(x) = \frac{1}{x + 6} \)

You are asked to evaluate \( \frac{f(x)}{g(x)} \) at \( x = -7 \).

### Step 1: Find \( f(-7) \)
Using the function \( f(x) = 2x \):
\[
f(-7) = 2(-7) = -14
\]

### Step 2: Find \( g(-7) \)
Using the function \( g(x) = |x - 5| \):
\[
g(-7) = |-7 - 5| = |-12| = 12
\]

### Step 3: Evaluate \( \frac{f(-7)}{g(-7)} \)
Now we compute the ratio:
\[
\frac{f(-7)}{g(-7)} = \frac{-14}{12} = \frac{-7}{6}
\]

Thus, \( \frac{f(-7)}{g(-7)} = \frac{-7}{6} \).

The answer is \( \boxed{\frac{-7}{6}} \).

Would you like a more detailed explanation or have further questions on this?

Here are 5 related questions to expand your understanding:
1. How do you find the absolute value of a number like in \( g(x) = |x - 5| \)?
2. What happens if \( g(x) \) equals 0 in the function \( \frac{f(x)}{g(x)} \)?
3. How would you evaluate \( h(x) \) for \( x = -7 \)?
4. Can \( h(x) = \frac{1}{x+6} \) ever be undefined?
5. How do we simplify the fraction \( \frac{-14}{12} \) to \( \frac{-7}{6} \)?

### Tip:
When simplifying fractions, always check for the greatest common divisor (GCD) between the numerator and denominator to reduce the fraction to its simplest form.

Evaluate the function (f/g)(-7) using the given functions: f(x) = 2x, g(x) = |x - 5|, h(x) = 1/(x + 6).

Learn how to evaluate the function (f/g)(x) using f(x) = 2x and g(x) = |x - 5| at x = -7. This problem covers key algebraic concepts such as absolute value and simplification of rational expressions, suitable for Grades 9-10.

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