https://file.aiquickdraw.com/mathbot/file/1728659615601gej0c6w7.jpg

Let's solve the equation: 

\[
7y + 6 = 5(y - 2)
\]

### Step-by-Step Solution:

1. Distribute the \(5\) on the right-hand side:
   \[
   7y + 6 = 5y - 10
   \]

2. Move the terms involving \(y\) to one side and the constant terms to the other side. Subtract \(5y\) from both sides:
   \[
   7y - 5y + 6 = -10
   \]
   Simplify:
   \[
   2y + 6 = -10
   \]

3. Subtract \(6\) from both sides:
   \[
   2y = -16
   \]

4. Finally, divide both sides by \(2\) to solve for \(y\):
   \[
   y = -8
   \]

### Solution:
\[
y = -8
\]

Would you like further details on any step, or do you have any questions?

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Here are 5 related questions you might find helpful:

1. How would you solve \(9x + 4 = 3(x - 2)\)?
2. What is the process for solving linear equations with variables on both sides?
3. Can you solve \(2a + 5 = 7a - 3\)?
4. What happens if you have a fraction in an equation, like \( \frac{4x}{3} + 1 = 2\)?
5. How can you check the solution of a linear equation after solving it?

### Tip:
Always check your final answer by substituting it back into the original equation to ensure it satisfies both sides.

Learn how to solve the linear equation 7y + 6 = 5(y - 2) with a detailed step-by-step guide. This problem involves key algebraic concepts, including distribution and variable isolation. Ideal for students in Grades 6-8.

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