https://file.aiquickdraw.com/mathbot/file/1725923675969h8hqk79j.jpg

The equation given in the image is:

\[
4y - 6y + 9y = -2
\]

Let's simplify the left-hand side of the equation:

\[
(4y - 6y + 9y) = (4 - 6 + 9)y = 7y
\]

So, the equation becomes:

\[
7y = -2
\]

To solve for \( y \), divide both sides by 7:

\[
y = \frac{-2}{7}
\]

Thus, the solution set of the equation is:

\[
\boxed{y = -\frac{2}{7}}
\]

Would you like more details on this solution? Here are five related questions:

1. How would you verify the solution to a linear equation?
2. What are the steps for simplifying expressions like \( 4y - 6y + 9y \)?
3. How does dividing both sides of an equation work when solving for a variable?
4. What are some common mistakes to avoid when simplifying linear equations?
5. Can you apply this method to solve more complex equations?

**Tip**: Always combine like terms first when solving algebraic equations to simplify the expression efficiently.

What is the solution set of the given equation? 4y - 6y + 9y = -2

Find the solution set for the linear equation 4y - 6y + 9y = -2. This problem involves key algebraic concepts, including simplifying expressions and solving linear equations. Ideal for students in Grades 6-8.

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