We can solve the equation step by step:

Given:

\[
7x - 2(x + 3) = (3x - 5) - 12
\]

### Step 1: Distribute the -2 on the left-hand side.
\[
7x - 2x - 6 = 3x - 5 - 12
\]

Simplify both sides:
\[
(7x - 2x) - 6 = 3x - 17
\]
\[
5x - 6 = 3x - 17
\]

### Step 2: Move all terms involving \( x \) to one side and constant terms to the other side.
\[
5x - 3x = -17 + 6
\]
\[
2x = -11
\]

### Step 3: Solve for \( x \).
\[
x = \frac{-11}{2}
\]
\[
x = -\frac{11}{2}
\]

Thus, the solution is \( x = -\frac{11}{2} \).

Would you like any additional details or explanations?

Here are 5 related questions to expand your knowledge:

1. How do you solve equations with variables on both sides?
2. How do you handle parentheses in algebraic expressions?
3. What are the steps for solving linear equations?
4. How do you check your solution for an equation?
5. What is the significance of combining like terms?

**Tip:** Always simplify both sides of an equation as much as possible before isolating the variable.

Step-by-step solution for solving the linear equation 7x - 2(x + 3) = (3x - 5) - 12. Learn how to apply the distributive property and combine like terms. Suitable for students in Grades 6-8.

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