how to remember how to solve -8y=48 kind of equations

To solve equations like \( -8y = 48 \), follow these simple steps:

### 1. **Isolate the Variable:**
   The goal is to get \( y \) by itself. In this case, \( y \) is being multiplied by \( -8 \), so you need to do the opposite (which is dividing) to both sides of the equation.

   \[
   \frac{-8y}{-8} = \frac{48}{-8}
   \]

### 2. **Simplify:**
   The division cancels out the \( -8 \) on the left-hand side, leaving just \( y \):

   \[
   y = \frac{48}{-8}
   \]

### 3. **Calculate:**
   Now perform the division:

   \[
   y = -6
   \]

So, the solution is \( y = -6 \).

### Tips for Remembering:
- **Inverse Operations**: Always remember that solving equations often requires undoing operations using their inverses (like division to undo multiplication).
- **Balance the Equation**: Whatever you do to one side, you must do to the other to maintain the equality.
- **Isolate the Variable**: The goal is to get the variable alone.
- **Check Your Work**: Substitute the value of \( y \) back into the original equation to verify it works.

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### Related Questions:
1. How do you solve equations when variables are on both sides?
2. What happens when the equation involves fractions?
3. How do you deal with equations involving parentheses?
4. Can I solve more complex equations involving powers?
5. What should I do when I encounter decimals in equations?

### Tip: 
Always perform the same operation on both sides of the equation to maintain the balance!

Learn how to solve linear equations like -8y = 48 with a simple, step-by-step approach. This problem emphasizes inverse operations, balancing equations, and isolating variables. Suitable for middle school students in Grades 6-8.

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