To solve for the value [tex]\( w \)[/tex] when the cost function [tex]\( C(w) = 230 \)[/tex], follow these steps:
1. Write down the given cost function:
[tex]\[
C(x) = 4x - 50
\][/tex]
2. Set the cost function equal to 230 since we need to find [tex]\( w \)[/tex] such that [tex]\( C(w) = 230 \)[/tex]:
[tex]\[
4w - 50 = 230
\][/tex]
3. Isolate the term with [tex]\( w \)[/tex] by adding 50 to both sides of the equation:
[tex]\[
4w - 50 + 50 = 230 + 50
\][/tex]
Simplifying, we get:
[tex]\[
4w = 280
\][/tex]
4. Solve for [tex]\( w \)[/tex] by dividing both sides of the equation by 4:
[tex]\[
w = \frac{280}{4}
\][/tex]
Simplifying, we get:
[tex]\[
w = 70
\][/tex]
Therefore, the value of [tex]\( w \)[/tex] is [tex]\( \boxed{70} \)[/tex].
