Consider the inequality 12 < −3(x+4). Which value of x is part of the solution set of this inequality?

We are given the inequality:

\[
12 < -3(x + 4)
\]

### Step 1: Distribute the \(-3\)
First, distribute the \(-3\) to both terms inside the parentheses:

\[
12 < -3x - 12
\]

### Step 2: Add 12 to both sides
Next, we add \(12\) to both sides to isolate the term with \(x\):

\[
12 + 12 < -3x
\]

\[
24 < -3x
\]

### Step 3: Divide by \(-3\)
Now, we divide both sides of the inequality by \(-3\). Remember, when dividing by a negative number, the inequality sign reverses:

\[
\frac{24}{-3} > x
\]

\[
-8 > x
\]

This means:

\[
x < -8
\]

### Conclusion:
Any value of \(x\) that is less than \(-8\) will be part of the solution set. For example, \(x = -9\) is a valid solution.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What happens if we divide an inequality by a negative number?
2. How would the solution change if the original inequality had a positive coefficient?
3. What is the graphical representation of the solution set on a number line?
4. Can you explain how to verify a solution by substituting values into the original inequality?
5. How do inequalities behave differently from equalities during operations?

**Tip:** Always reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Learn how to solve the inequality 12 < −3(x+4) with a detailed solution. This covers key algebraic concepts like the distributive property and the rules for solving inequalities, including reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 8-10.

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