1. **State the problem:** Solve the equation $$3x + 12 = 21$$ for $$x$$. 2. **Formula and rules:** To solve a linear equation like $$ax + b = c$$, isolate $$x$$ by performing inverse operations: subtract $$b$$ from both sides, then divide both sides by $$a$$. 3. **Step-by-step solution:** 1. Start with the equation: $$3x + 12 = 21$$ 2. Subtract 12 from both sides to isolate the term with $$x$$: $$3x + \cancel{12} - \cancel{12} = 21 - 12$$ $$3x = 9$$ 3. Divide both sides by 3 to solve for $$x$$: $$\frac{3x}{\cancel{3}} = \frac{9}{\cancel{3}}$$ $$x = 3$$ 4. **Answer:** The solution is $$x = 3$$. This method applies to all similar linear equations: isolate the variable term, then divide by its coefficient. q_count is 1 because only the first problem is solved as per instructions.