We are given the function $f(x) = 2x^3 + qx + 2$, where $q$ is a constant. We are also given that $f(-1) = 2$. We need to find the value of $q$.

1. Problem Description

We are given the function $f(x) = 2x^3 + qx + 2$, where $q$ is a constant. We are also given that $f(-1) = 2$. We need to find the value of $q$.

2. Solution Steps

We substitute $x = -1$ into the expression for $f(x)$:

$f(-1) = 2(-1)^3 + q(-1) + 2$

Since we know that $f(-1) = 2$, we can write:

$2 = 2(-1)^3 + q(-1) + 2$

$2 = 2(-1) - q + 2$

$2 = -2 - q + 2$

$2 = -q$

Multiply both sides by -1:

$-2 = q$

Therefore, $q = -2$.

3. Final Answer

$q = -2$