Sure, let's solve the problem step-by-step:
Given the linear function [tex]\( f(x) = -4x + 8 \)[/tex], we need to find the value of [tex]\( x \)[/tex] when [tex]\( f(x) = 24 \)[/tex].
1. Start with the equation for [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = -4x + 8
\][/tex]
2. Set [tex]\( f(x) \)[/tex] equal to 24:
[tex]\[
-4x + 8 = 24
\][/tex]
3. To isolate the term involving [tex]\( x \)[/tex], subtract 8 from both sides of the equation:
[tex]\[
-4x = 24 - 8
\][/tex]
[tex]\[
-4x = 16
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by -4:
[tex]\[
x = \frac{16}{-4}
\][/tex]
[tex]\[
x = -4
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( f(x) = 24 \)[/tex] is [tex]\( x = -4 \)[/tex].
Therefore, the correct answer is [tex]\( x = -4 \)[/tex].
