Let's solve the equation step by step:

\[
3(2 - x) + 10 = 12 - x(3) + 4
\]

### Step 1: Expand both sides of the equation
- On the left-hand side:  
\[
3(2 - x) = 6 - 3x
\]
So the left-hand side becomes:  
\[
6 - 3x + 10 = 16 - 3x
\]

- On the right-hand side:  
\[
12 - x(3) = 12 - 3x
\]
So the right-hand side becomes:  
\[
12 - 3x + 4 = 16 - 3x
\]

### Step 2: Combine like terms on both sides
- Left-hand side:  
\[
6 + 10 - 3x = 16 - 3x
\]
This simplifies to:  
\[
16 - 3x = 16 - 3x
\]

### Step 3: Analyze the simplified equation
The equation is now:  
\[
16 - 3x = 16 - 3x
\]
This is a **true statement**, meaning the equation holds for all values of \( x \).

### Conclusion:
The equation is an identity, which means that **any value of \( x \) will satisfy the equation**.

### Would you like more details or have any questions?

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Here are 5 related questions:
1. What are the steps to solve equations with distributive properties?
2. How do you determine if an equation has infinite solutions?
3. How can you check the solution to an equation?
4. What does it mean for an equation to be an identity?
5. How do you solve equations with variables on both sides?

**Tip:** Always simplify both sides of an equation as much as possible before solving!

Learn how to solve the linear equation 3(2-x) + 10 = 12 - x(3) + 4 step by step. This detailed solution covers key algebraic concepts such as the distributive property and how to identify an identity equation. Suitable for students in Grades 8-10.

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