Given g, of, x, equals, minus, x, plus, 5*g*(*x*)=−*x*+5, solve for x*x* when g, of, x, equals, minus, 2*g*(*x*)=−2.

To solve for \(x\) when \(g(x) = -2\) and the function is given by:

\[
g(x) = -x + 5
\]

we need to set the equation equal to \(-2\) and solve for \(x\).

### Step-by-step solution:

1. Set \(g(x) = -2\):

\[
-x + 5 = -2
\]

2. Subtract 5 from both sides:

\[
-x = -2 - 5
\]

\[
-x = -7
\]

3. Multiply both sides by \(-1\) to solve for \(x\):

\[
x = 7
\]

### Solution:

\[
x = 7
\]

Would you like more details or have any questions?

### Related Questions:

1. What is the value of \(x\) when \(g(x) = 0\)?
2. How do you find the inverse of \(g(x) = -x + 5\)?
3. What is the slope of the line represented by \(g(x) = -x + 5\)?
4. If \(g(x) = -x + 5\), what is \(g(3)\)?
5. What is the y-intercept of the function \(g(x) = -x + 5\)?

**Tip:** When working with linear functions, remember that the coefficient of \(x\) represents the slope, and the constant term represents the y-intercept.

Learn how to solve for x in the linear equation g(x) = -x + 5 when g(x) equals -2. This problem involves solving a linear equation and understanding the concept of function values. Suitable for high school students.

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