https://file.aiquickdraw.com/mathbot/file/1727193520119s422j1ln.jpg

The equation given in the image is:

\[ -12y - 19 = -14y + 9 \]

To solve for \( y \), let's first simplify and rearrange the terms.

1. Add \( 14y \) to both sides to eliminate \( y \) from the right side:
\[ -12y + 14y - 19 = 9 \]
\[ 2y - 19 = 9 \]

2. Add 19 to both sides to isolate \( 2y \):
\[ 2y - 19 + 19 = 9 + 19 \]
\[ 2y = 28 \]

3. Divide both sides by 2 to solve for \( y \):
\[ y = \frac{28}{2} \]
\[ y = 14 \]

Therefore, \( y = 14 \).

Would you like more details or have any other questions? Here are some related topics to consider:
1. What would be the steps to solve for \( y \) if both sides were multiplied by a factor before solving?
2. How would you verify the solution of this equation?
3. What is the importance of maintaining balance on both sides of an equation when solving for a variable?
4. Can you provide examples of similar equations but with different operations, like addition or multiplication?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always check your final answer by plugging it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation -12y - 19 = -14y + 9. This step-by-step solution involves simplifying, combining like terms, and isolating the variable y. Suitable for students in Grades 7-9.

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