$$ {\displaylines3x+6-x\le12\\ \placeholder{}} $$

To solve the inequality $3x + 6 - x \leq 12$, follow these steps:

1. **Combine like terms** on the left side:
   \[
   (3x - x) + 6 \leq 12
   \]
   which simplifies to:
   \[
   2x + 6 \leq 12
   \]

2. **Subtract 6 from both sides** to isolate the term with $x$:
   \[
   2x \leq 6
   \]

3. **Divide both sides by 2** to solve for $x$:
   \[
   x \leq 3
   \]

So the solution to the inequality is $x \leq 3$.

Would you like further details on any of these steps, or do you have any questions?

Here are 5 related questions for practice:
1. Solve the inequality $4x + 5 \geq 3x + 9$.
2. Solve the inequality $5x - 7 \leq 2x + 11$.
3. Solve the inequality $7x - 4 > 3x + 8$.
4. Solve the compound inequality $x - 3 \leq 2 \text{ and } x + 4 > 7$.
5. Graph the solution to the inequality $x \leq 3$ on a number line.

**Tip:** When solving inequalities, remember that if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

Learn how to solve the inequality 3x + 6 - x ≤ 12 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequalities and basic algebraic operations. Suitable for students in Grades 7-9.

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