We are given the function $g(x) = -2x + 1$ and asked to solve for $x$ when $g(x) = 5$.

Step 1: Set the equation equal to 5

We know that $g(x) = -2x + 1$, and we are asked to find $x$ when $g(x) = 5$. So, we substitute 5 into the equation:

$5 = -2x + 1$

Step 2: Solve for $x$

Now, solve for $x$.

1. Subtract 1 from both sides:

$5 - 1 = -2x$

$4 = -2x$

2. Divide both sides by -2:

$x = \frac{4}{-2}$

$x = -2$

Final Answer:

$x = -2$

Let me know if you'd like more details or have any questions!

Here are 5 related questions you can explore:

1. How do you solve linear equations with variables on both sides?
2. What is the slope of the function $g(x) = -2x + 1$?
3. How can you graph the function $g(x) = -2x + 1$?
4. What happens if we solve for $g(x) = 0$ instead of 5?
5. How would you solve a system of equations involving $g(x)$?

Tip: Always double-check your algebraic steps to ensure accuracy, especially when isolating the variable.