Let's start by calculating the values for $f(x) = 3x - 2$ and $g(x) = -2x$ for the given values of $x$. I'll fill in the table and then determine where $f(x) = g(x)$.

1. For $x = -1$:

• $f(-1) = 3(-1) - 2 = -3 - 2 = -5$
• $g(-1) = -2(-1) = 2$

2. For $x = 0$:

• $f(0) = 3(0) - 2 = -2$
• $g(0) = -2(0) = 0$

3. For $x = 1$:

• $f(1) = 3(1) - 2 = 3 - 2 = 1$
• $g(1) = -2(1) = -2$

4. For $x = 2$:

• $f(2) = 3(2) - 2 = 6 - 2 = 4$
• $g(2) = -2(2) = -4$

5. For $x = 3$:

• $f(3) = 3(3) - 2 = 9 - 2 = 7$
• $g(3) = -2(3) = -6$

Completed Table:

$x$	$f(x) = 3x - 2$	$g(x) = -2x$
-1	-5	2
0	-2	0
1	1	-2
2	4	-4
3	7	-6

Now, to find where $f(x) = g(x)$:

We want to solve $3x - 2 = -2x$.

• Adding $2x$ to both sides:
  $3x + 2x - 2 = 0 \quad \Rightarrow \quad 5x - 2 = 0$
• Adding $2$ to both sides:
  $5x = 2$
• Dividing both sides by $5$:
  $x = \frac{2}{5}$

Thus, the equation $f(x) = g(x)$ has a solution at $x = \frac{2}{5}$, which does not appear directly in the table but is the exact solution for when $f(x) = g(x)$.

Would you like more details or have any further questions? Here are 5 related questions for you:

1. How would you solve for $x$ in equations with different linear functions like $f(x) = 2x + 3$ and $g(x) = 4x - 1$?
2. How can you graph the two functions $f(x) = 3x - 2$ and $g(x) = -2x$?
3. What is the general method for finding where two linear functions intersect?
4. How can you apply this process to non-linear equations?
5. What happens when two functions are parallel, and they never intersect?

Tip: When solving for where two linear functions are equal, always isolate $x$ to find the point of intersection. If the functions are parallel, they will not intersect.