https://file.aiquickdraw.com/mathbot/file/1726260149043yzjiq95n.jpg

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!

If g(x) = 2x − |5 + x|, find g(10) and g(−7).

Solve the function g(x) = 2x − |5 + x| by calculating g(10) and g(−7). This problem covers algebraic concepts such as absolute value and linear functions, suitable for students in Grades 8-10. Step-by-step solution provided.

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