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Let's solve the equation step by step. The given equation is:

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

### Step 1: Combine like terms on both sides of the equation.
Start by moving all terms involving \( d \) to one side and constant terms to the other side.

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

This simplifies to:

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

### Step 2: Simplify the expression for \( d \) on the right-hand side.
Add the terms involving \( d \):

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

Now, the equation becomes:

\[
-1 = 2d
\]

### Step 3: Solve for \( d \).

Divide both sides by 2:

\[
d = \frac{-1}{2}
\]

Thus, the solution is:

\[
d = -\frac{1}{2}
\]

Would you like further details or explanations? Here are five related questions for further exploration:

1. What are the steps to solve a linear equation with fractions?
2. How can you check the solution of this equation?
3. What happens if both sides of the equation had variables only?
4. How would this problem change if \( d \) were squared?
5. How does solving an equation with fractions differ from solving an equation with decimals?

**Tip**: When solving equations with fractions, it's often helpful to eliminate fractions early by multiplying the entire equation by a common denominator!

Learn how to solve the linear equation involving fractions: 3 - (1/2)d = (3/2)d + 4 - d. This detailed step-by-step guide breaks down the solution and simplifies the equation. Suitable for students in Grades 7-9.

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