Let's solve the inequality step by step.

Given inequality:

$3(x + 3) - 3 > -3(x - 4) + 12$

Step 1: Distribute the constants on both sides.

$3x + 9 - 3 > -3x + 12 + 12$ Simplifying: $3x + 6 > -3x + 24$

Step 2: Add $3x$ to both sides to move all $x$-terms to one side.

$3x + 3x + 6 > 24$ This simplifies to: $6x + 6 > 24$

Step 3: Subtract 6 from both sides.

$6x > 18$

Step 4: Divide by 6.

$x > 3$

Final answer:

The solution to the inequality is: $x > 3$

Would you like any further explanation or details on this?

Here are five related questions:

1. What happens if we reverse the inequality sign in the problem?
2. How do we solve inequalities involving fractions?
3. How do we handle inequalities with absolute values?
4. Can this type of inequality be graphed on a number line?
5. What would change if we had to divide or multiply by a negative number?

Tip: Always remember to flip the inequality sign when multiplying or dividing by a negative number in inequalities!