To solve the equation \( 15 - 2y = 5y - 2 \), we can follow these steps:

### Step 1: Move all terms involving \( y \) to one side.
\[
15 - 2y = 5y - 2
\]
Add \( 2y \) to both sides to move the \( -2y \) from the left side:
\[
15 = 7y - 2
\]

### Step 2: Move constants to the other side.
Add \( 2 \) to both sides to move the constant \( -2 \) from the right side:
\[
15 + 2 = 7y
\]
\[
17 = 7y
\]

### Step 3: Solve for \( y \).
Now divide both sides by \( 7 \):
\[
y = \frac{17}{7}
\]

So, the solution is \( y = \frac{17}{7} \).

Would you like more details on any of the steps or have any questions?

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Here are five related questions:
1. How would you solve \( 10 - 3x = 4x + 1 \)?
2. What is the general approach to solving linear equations?
3. How do you handle equations with variables on both sides?
4. What happens when an equation has no solutions?
5. How do you verify the solution of an equation?

**Tip:** Always check your solution by substituting the value back into the original equation!

Learn how to solve the linear equation 15 - 2y = 5y - 2 with a step-by-step guide. This problem covers key algebraic concepts like isolating variables and balancing equations. Suitable for students in Grades 6-8.

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