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Let's solve the equation for \( d \):

The equation provided is:

\[
-\frac{1}{2}d + \frac{3}{8} - d = \frac{1}{4} + \frac{3}{4}d + 2
\]

### Step 1: Combine like terms
First, collect all the terms involving \( d \) on one side and the constant terms on the other side. Start by simplifying both sides.

On the left side:
\[
-\frac{1}{2}d - d = -\frac{1}{2}d - \frac{2}{2}d = -\frac{3}{2}d
\]

So, the left-hand side becomes:
\[
-\frac{3}{2}d + \frac{3}{8}
\]

On the right side, there's no need to combine terms since \( \frac{3}{4}d + 2 + \frac{1}{4} \) is already simplified.

Thus, the equation becomes:
\[
-\frac{3}{2}d + \frac{3}{8} = \frac{1}{4} + \frac{3}{4}d + 2
\]

### Step 2: Eliminate the fractions
To eliminate the fractions, multiply the entire equation by 8, which is the least common denominator of 2, 4, and 8.

Multiplying through by 8:
\[
8\left(-\frac{3}{2}d\right) + 8\left(\frac{3}{8}\right) = 8\left(\frac{1}{4}\right) + 8\left(\frac{3}{4}d\right) + 8(2)
\]

This simplifies to:
\[
-12d + 3 = 2 + 6d + 16
\]

### Step 3: Simplify the equation
Now simplify both sides:
\[
-12d + 3 = 6d + 18
\]

### Step 4: Move the variable terms to one side
Add \( 12d \) to both sides to move all \( d \)-terms to the right:
\[
3 = 18d + 18
\]

### Step 5: Isolate the variable
Subtract 18 from both sides:
\[
-15 = 18d
\]

Now, divide both sides by 18:
\[
d = \frac{-15}{18} = \frac{-5}{6}
\]

### Final Answer:
\[
d = -\frac{5}{6}
\]

Would you like more details on this solution? Let me know if you have any questions!

Here are 5 related questions to expand your understanding:
1. How can you handle equations with multiple fractions more easily?
2. What is the least common denominator (LCD), and why is it useful when solving equations with fractions?
3. How do you isolate a variable when it's on both sides of the equation?
4. What are some alternative methods for solving linear equations involving fractions?
5. Can you check if \( d = -\frac{5}{6} \) satisfies the original equation?

**Tip:** When working with fractions, multiplying the entire equation by the least common denominator helps clear the fractions and simplifies the solving process.

Solve for d: -1/2 d + 3/8 - d = 1/4 + 3/4 d + 2

Learn how to solve the linear equation involving fractions: -1/2 d + 3/8 - d = 1/4 + 3/4 d + 2. This problem covers key algebraic concepts, including solving equations with fractions, and is suitable for students in Grades 8-10.

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