Question

The output of a function is 7 more than 3 times the input. Find the input when the output is -8.

Answer 1

Let's define the input as \( x \) and the output as \( y \). According to the problem, the relationship between the output and the input is given by the equation:

\[
y = 3x + 7
\]

We need to find the input \( x \) when the output \( y \) is -8. We can set up the equation:

\[
-8 = 3x + 7
\]

To solve for \( x \), we first isolate the term containing \( x \). We can do this by subtracting 7 from both sides:

\[
-8 - 7 = 3x
\]

This simplifies to:

\[
-15 = 3x
\]

Now, we can solve for \( x \) by dividing both sides by 3:

\[
x = \frac{-15}{3} = -5
\]

Thus, the input \( x \) when the output is -8 is

\[
\boxed{-5}
\]

To confirm, we can substitute \( x = -5 \) back into the original equation to check if the output is indeed -8:

\[
y = 3(-5) + 7 = -15 + 7 = -8
\]

This is correct, so the solution is verified. The input is \( \boxed{-5} \).