Let's solve the inequality \(-6x + 3(x + 5) > 4 - 3x\).

### Step 1: Distribute the 3 on the left side.
\[
-6x + 3(x + 5) = -6x + 3x + 15
\]

### Step 2: Combine like terms on the left side.
\[
-6x + 3x + 15 = -3x + 15
\]

So the inequality now is:
\[
-3x + 15 > 4 - 3x
\]

### Step 3: Add \(3x\) to both sides to eliminate \(-3x\).
\[
15 > 4
\]

### Step 4: Analyze the result.
The inequality \(15 > 4\) is always true for any value of \(x\). This means that the original inequality is true for all values of \(x\).

### Final Answer:
The solution to the inequality is \(x \in \mathbb{R}\), meaning all real numbers satisfy the inequality.

Would you like further details on any step, or do you have questions?

### Related Questions:
1. What are the steps to solve a linear inequality with variables on both sides?
2. How do you handle inequalities with distribution and combination of like terms?
3. What happens if we get a false statement like \(0 > 5\) after simplifying an inequality?
4. Can you explain what it means when an inequality is true for all real numbers?
5. How would you graph the solution of this inequality on a number line?

### Tip:
When solving inequalities, always check if the final statement is true or false to determine if the solution is all real numbers or no solution.

Learn how to solve the inequality -6x + 3(x + 5) > 4 - 3x with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequalities, the distributive property, and combining like terms. Suitable for students in Grades 7-9.

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