The inequality is:

\[
12x + 12 < -12y + 12
\]

Let's solve this step by step.

### Step 1: Simplify both sides
First, subtract \( 12 \) from both sides to remove the constant on the right-hand side:

\[
12x + 12 - 12 < -12y + 12 - 12
\]

This simplifies to:

\[
12x < -12y
\]

### Step 2: Divide both sides by 12
Now, divide both sides of the inequality by 12:

\[
x < -y
\]

### Final Answer:
The solution to the inequality is:

\[
x < -y
\]

This means that \( x \) must be less than the negative of \( y \).

Do you need more details or have any questions?  
Here are 5 related questions you might want to explore:

1. How do you graph the inequality \( x < -y \)?
2. How does dividing or multiplying by a negative number affect inequalities?
3. What is the difference between \( x < -y \) and \( x > -y \)?
4. How can inequalities be used to define regions on a coordinate plane?
5. Can you solve an inequality with more complex terms, such as \( x^2 + 12x < -y^2 + 3y \)?

**Tip:** When dividing or multiplying both sides of an inequality by a negative number, always remember to flip the inequality sign!

Learn how to solve the linear inequality 12x + 12 < -12y + 12 with a step-by-step solution. This problem covers key algebraic concepts, including simplification and solving linear inequalities. Suitable for students in Grades 7-9.

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