To solve the equation \(3(d-1) + 4 = -2d\), we'll follow the steps to simplify and isolate the variable \(d\).

### Step-by-Step Solution

1. **Expand the equation**:  
   Distribute the \(3\) across the terms inside the parentheses:

   \[
   3 \cdot d - 3 \cdot 1 + 4 = -2d
   \]

   Simplifying this gives:

   \[
   3d - 3 + 4 = -2d
   \]

2. **Combine like terms**:  
   Combine the constants \(-3\) and \(4\):

   \[
   3d + 1 = -2d
   \]

3. **Isolate \(d\)**:  
   To isolate \(d\), add \(2d\) to both sides:

   \[
   3d + 2d + 1 = -2d + 2d
   \]

   Simplifying this gives:

   \[
   5d + 1 = 0
   \]

4. **Solve for \(d\)**:  
   Subtract \(1\) from both sides:

   \[
   5d = -1
   \]

   Divide both sides by \(5\) to solve for \(d\):

   \[
   d = -\frac{1}{5}
   \]

### Solution

The solution to the equation \(3(d-1) + 4 = -2d\) is:

\[
d = -\frac{1}{5}
\]

Would you like more details or have any questions?

Here are some related questions to explore:

1. What would the solution be if the equation were \(3(d-1) + 4 = 2d\)?
2. How do you solve an equation with variables on both sides?
3. What happens if we change the constant term in the equation?
4. How do you check if your solution to an equation is correct?
5. Can you explain the importance of combining like terms in solving equations?

**Tip:** When solving equations, always perform the same operation on both sides to maintain the balance.

Learn how to solve the equation 3(d-1) + 4 = -2d step-by-step with detailed explanations. This problem involves solving linear equations using distribution and combining like terms. Suitable for students in Grades 7-9.

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