Let's solve the equation:

\[
3(x - 2) + 5(2 - x) = 16
\]

### Step 1: Expand both sides
First, distribute the constants inside the parentheses:

\[
3(x - 2) = 3x - 6
\]
\[
5(2 - x) = 10 - 5x
\]

Now, the equation becomes:

\[
3x - 6 + 10 - 5x = 16
\]

### Step 2: Combine like terms
Group the \(x\) terms and the constant terms:

\[
(3x - 5x) + (-6 + 10) = 16
\]
\[
-2x + 4 = 16
\]

### Step 3: Solve for \(x\)
Subtract 4 from both sides:

\[
-2x = 16 - 4
\]
\[
-2x = 12
\]

Now, divide by \(-2\):

\[
x = \frac{12}{-2}
\]
\[
x = -6
\]

Thus, the solution is \(x = -6\).

---

Would you like further details or explanations? Here are five related questions:

1. How would the solution change if the equation was \(3(x - 2) + 5(2 - x) = 20\)?
2. What are the steps to verify the solution \(x = -6\) in the original equation?
3. How do we handle equations with variables on both sides?
4. What would happen if one of the coefficients were a fraction?
5. Can you solve a similar equation, \(4(x + 1) - 3(2x - 5) = 18\)?

**Tip:** Always double-check your distribution and combining of like terms when solving equations to avoid mistakes.

Learn how to solve the linear equation 3(x-2)+5(2-x)=16 with detailed steps, including using the distributive property and combining like terms. This problem is ideal for students in Grades 6-8, covering fundamental algebraic techniques.

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