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The problem asks us to find the value of \( x \) for the function \( f(x) = 3x - 2 \) when \( f(x) = 16 \).

We can solve this by setting the function equal to 16 and solving for \( x \):

\[
f(x) = 3x - 2
\]
\[
16 = 3x - 2
\]

Now, solve for \( x \):

1. Add 2 to both sides:
\[
16 + 2 = 3x
\]
\[
18 = 3x
\]

2. Divide both sides by 3:
\[
x = \frac{18}{3}
\]
\[
x = 6
\]

So, the value of \( x \) is 6.

Would you like any further details or clarifications on this solution?

Here are 5 related questions to expand on this concept:
1. How would the solution change if \( f(x) = 5x - 4 \) and \( f(x) = 21 \)?
2. What is the graphical interpretation of solving \( f(x) = 3x - 2 \) for \( x \)?
3. How can you determine if \( f(x) = 3x - 2 \) is an increasing or decreasing function?
4. How would you solve for \( x \) if \( f(x) = 3x - 2 \) and \( f(x) = 0 \)?
5. How does solving \( f(x) = 3x - 2 \) differ from solving a quadratic equation?

**Tip**: Always check your solution by substituting the found value of \( x \) back into the original function to confirm it satisfies the equation!

For the function f(x) = 3x - 2, find the matching value for x when f(x) = 16.

Learn how to solve the linear equation f(x) = 3x - 2 when f(x) equals 16. This problem involves basic algebraic operations and is suitable for students in Grades 6-8.

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