To solve for [tex]\( x \)[/tex] given the function [tex]\( f(x) = 6x + 1 \)[/tex] and the equation [tex]\( f(x) = -11 \)[/tex]:
1. Start with the equation given by the problem:
[tex]\[
f(x) = -11
\][/tex]
2. Substitute [tex]\( f(x) \)[/tex] with [tex]\( 6x + 1 \)[/tex]:
[tex]\[
6x + 1 = -11
\][/tex]
3. To isolate [tex]\( x \)[/tex], first subtract 1 from both sides of the equation:
[tex]\[
6x + 1 - 1 = -11 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
6x = -12
\][/tex]
4. Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 6:
[tex]\[
x = \frac{-12}{6}
\][/tex]
5. Simplify the result:
[tex]\[
x = -2
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( -2 \)[/tex].
