The function given is:

$g(x) = 2x - |5 + x|$

We need to evaluate this function for two values: $g(10)$ and $g(-7)$.

Step 1: Calculate $g(10)$

Substitute $x = 10$ into the function:

$g(10) = 2(10) - |5 + 10|$ $g(10) = 20 - |15|$ Since $|15| = 15$, we have: $g(10) = 20 - 15 = 5$

Step 2: Calculate $g(-7)$

Substitute $x = -7$ into the function:

$g(-7) = 2(-7) - |5 + (-7)|$ $g(-7) = -14 - |5 - 7|$ $g(-7) = -14 - |-2|$ Since $|-2| = 2$, we have: $g(-7) = -14 - 2 = -16$

Final Answers:

$g(10) = 5$ $g(-7) = -16$

Would you like more details on the steps? Here are five related questions to explore further:

1. How would the function behave for negative values of $x$?
2. What happens if the absolute value term is removed? How does the function change?
3. Can you graph the function $g(x) = 2x - |5 + x|$ for a range of values?
4. What is the domain and range of $g(x)$?
5. How does the function behave as $x$ approaches positive and negative infinity?

Tip: The absolute value function is piecewise. Understanding how it behaves for different signs of $x$ can help when solving more complex equations!