To find the value of [tex]\( x \)[/tex] for which the function [tex]\( g(x) = -5x + 1 \)[/tex] equals [tex]\(-9\)[/tex], follow these steps:
1. Start by setting the function [tex]\( g(x) \)[/tex] equal to [tex]\(-9\)[/tex]:
[tex]\[
g(x) = -9
\][/tex]
2. Substitute [tex]\( g(x) \)[/tex] with [tex]\(-5x + 1\)[/tex]:
[tex]\[
-5x + 1 = -9
\][/tex]
3. Next, isolate the term containing [tex]\( x \)[/tex]. Begin by subtracting 1 from both sides of the equation:
[tex]\[
-5x = -9 - 1
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
-5x = -10
\][/tex]
4. Now, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\(-5\)[/tex]:
[tex]\[
x = \frac{-10}{-5}
\][/tex]
5. Perform the division:
[tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] for which [tex]\( g(x) = -9 \)[/tex] is [tex]\( x = 2 \)[/tex].
