To determine the value of \( x \) for which \( f(x) = 35 \) given the linear function \( f(x) = -5x + 10 \), follow these steps:
1. Start with the equation defined by the function:
[tex]\[
f(x) = -5x + 10
\][/tex]
2. Set \( f(x) \) equal to 35:
[tex]\[
-5x + 10 = 35
\][/tex]
3. Isolate the term involving \( x \) by subtracting 10 from both sides of the equation:
[tex]\[
-5x + 10 - 10 = 35 - 10
\][/tex]
Which simplifies to:
[tex]\[
-5x = 25
\][/tex]
4. Solve for \( x \) by dividing both sides by -5:
[tex]\[
x = \frac{25}{-5}
\][/tex]
Which simplifies to:
[tex]\[
x = -5
\][/tex]
Given that \( x = -5 \) is the solution, we can check our answer by substituting \( x = -5 \) back into the original function:
[tex]\[
f(-5) = -5(-5) + 10 = 25 + 10 = 35
\][/tex]
Indeed, \( f(x) = 35 \) when \( x = -5 \).
Thus, the correct value of \( x \) is:
[tex]\[
\boxed{-5}
\][/tex]
