The inequality you've written is:

$2(6 + x) \geq 13 - 3x$

Step-by-step solution:

1. Distribute the 2 on the left-hand side: $2 \cdot 6 + 2 \cdot x \geq 13 - 3x$ This simplifies to: $12 + 2x \geq 13 - 3x$

2. Move all terms with $x$ to one side and the constants to the other side: $2x + 3x \geq 13 - 12$ Simplifying: $5x \geq 1$

3. Solve for $x$ by dividing both sides by 5: $x \geq \frac{1}{5}$

Final Answer:

$x \geq \frac{1}{5}$

This means the solution to the inequality is any $x$ that is greater than or equal to $\frac{1}{5}$.

Would you like more details or have any questions about this solution?

Related Questions:

1. How do you solve inequalities with negative coefficients?
2. What happens if you divide by a negative number in inequalities?
3. How do you represent solutions to inequalities on a number line?
4. Can inequalities be solved using graphing methods?
5. What are the different ways to express inequality solutions (e.g., interval notation)?

Tip:

When solving inequalities, always reverse the inequality sign if you multiply or divide by a negative number.