https://file.aiquickdraw.com/mathbot/file/1729794777245t307kub3.jpg

The equation presented in the image is:

\[
3 - \frac{1}{2}d = \frac{3}{2}d + 4 - d
\]

### Steps to solve for \(d\):

1. **Combine like terms on both sides**:
   Start by eliminating the fractions. Multiply the entire equation by 2 to clear the denominators:

   \[
   2 \times \left( 3 - \frac{1}{2}d \right) = 2 \times \left( \frac{3}{2}d + 4 - d \right)
   \]

   This simplifies to:

   \[
   6 - d = 3d + 8 - 2d
   \]

2. **Simplify the equation**:
   Combine like terms on the right-hand side:

   \[
   6 - d = d + 8
   \]

3. **Move all terms involving \(d\) to one side**:
   Subtract \(d\) from both sides:

   \[
   6 - d - d = 8
   \]

   Simplifies to:

   \[
   6 - 2d = 8
   \]

4. **Solve for \(d\)**:
   Subtract 6 from both sides:

   \[
   -2d = 2
   \]

   Now, divide by -2:

   \[
   d = -1
   \]

### Final answer:
\[
d = -1
\]

Let me know if you'd like further details or clarifications.

---

Here are 5 related questions to further explore this concept:

1. What happens if both sides of the equation include variables with different coefficients?
2. How would you solve the same equation if there were no fractions to begin with?
3. How can you verify your solution once you've found \(d\)?
4. What role does the distributive property play in solving equations like these?
5. How would you handle equations with more complex terms, such as square roots?

**Tip**: Always try to clear fractions or decimals early in the equation to simplify your work and reduce calculation errors.

Learn how to solve the linear equation 3 - (1/2)d = (3/2)d + 4 - d with a step-by-step approach. This problem explores key algebraic concepts like combining like terms and balancing equations, suitable for Grades 8-10.

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