To determine the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = -12 \)[/tex] given the function [tex]\( f(x) = 2 - 7x \)[/tex], let's follow these steps:
1. Start with the given function and the target value:
[tex]\[
f(x) = 2 - 7x
\][/tex]
[tex]\[
f(x) = -12
\][/tex]
2. Set the function equal to the target value:
[tex]\[
2 - 7x = -12
\][/tex]
3. Isolate the term involving [tex]\( x \)[/tex]. To do this, subtract 2 from both sides of the equation:
[tex]\[
2 - 7x - 2 = -12 - 2
\][/tex]
Simplifying this, we get:
[tex]\[
-7x = -14
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by -7:
[tex]\[
x = \frac{-14}{-7}
\][/tex]
5. Simplify the division:
[tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies [tex]\( f(x) = -12 \)[/tex] is [tex]\( x = 2 \)[/tex].
