https://file.aiquickdraw.com/mathbot/file/1726797848683fp9tnq81.jpg

The equation provided is:

\[
2y + 6 = 2(1 + 2y)
\]

The steps shown involve dividing both sides by 2 to simplify:

\[
\frac{2y + 6}{2} = \frac{2(1 + 2y)}{2}
\]

This simplifies to:

\[
y + 3 = 1 + 2y
\]

Next, subtract \(y\) from both sides to isolate the terms involving \(y\):

\[
3 = 1 + y
\]

Finally, subtract 1 from both sides to solve for \(y\):

\[
2 = y
\]

Thus, the solution is \(y = 2\).

Would you like more details on any part of the process, or do you have any further questions?

Here are 5 follow-up questions to extend understanding:
1. How do you handle equations with multiple variables on both sides?
2. Can you always divide an equation by a constant? What happens if you divide by zero?
3. What methods can be used to verify the solution?
4. How does distributing work in more complex equations?
5. What if the equation included fractions from the beginning?

**Tip:** When solving equations, always try to simplify both sides before making any operations to isolate the variable.

Solve the equation 2y + 6 = 2(1 + 2y) and simplify.

Learn how to solve the linear equation 2y + 6 = 2(1 + 2y) by simplifying and isolating the variable y. This problem introduces algebraic concepts related to solving for variables on both sides. Suitable for students in Grades 6-8.

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