To solve this question, let’s go through each of Heidi's steps in solving the equation and provide justifications for each.

The equation is:

$3(x + 4) + 2 = 2 + 5(x - 4)$

Step-by-Step Justification:

1. Step 1: $3x + 12 + 2 = 2 + 5x - 20$

   • Justification: This step involves Distributive Property. Heidi distributed $3$ to both $x$ and $4$ on the left side, and $5$ to both $x$ and $-4$ on the right side.

2. Step 2: $3x + 14 = 5x - 18$

   • Justification: This step is Combining Like Terms. Heidi combined $12 + 2$ to get $14$ on the left side and combined $2 - 20$ to get $-18$ on the right side.

3. Step 3: $14 = 2x - 18$

   • Justification: This step involves Subtracting $3x$ from Both Sides. Heidi moved $3x$ from the left side to the right by subtracting it from both sides, simplifying $5x - 3x$ to $2x$.

4. Step 4: $32 = 2x$

   • Justification: This step is Adding 18 to Both Sides. Heidi added $18$ to both sides to isolate terms involving $x$.

5. Step 5: $16 = x$

   • Justification: This step is Dividing Both Sides by 2. Heidi divided both sides by $2$ to solve for $x$.

These justifications explain how Heidi arrived at each step in her solution.

Would you like further details or explanations on any part of the solution?

Here are 5 related questions to expand understanding:

1. How would the solution change if the constants in the equation were different?
2. What is the importance of following the order of operations in solving equations?
3. How can you check if the solution for $x$ is correct in the original equation?
4. What is the distributive property, and why is it important in solving equations?
5. Can this problem be solved by a different method, such as graphing?

Tip: When solving equations, always check each step to ensure all operations are correct, as small mistakes can lead to incorrect solutions.