We need to solve the equation:

$\frac{1}{2}x + \frac{3}{2} = \frac{3}{8}x - 6$

Step 1: Eliminate the fractions by multiplying through by 8 (the least common denominator).

Multiply both sides of the equation by 8:

$8 \times \left( \frac{1}{2}x + \frac{3}{2} \right) = 8 \times \left( \frac{3}{8}x - 6 \right)$

This simplifies to:

$4x + 12 = 3x - 48$

Step 2: Move all terms involving $x$ to one side and constants to the other.

Subtract $3x$ from both sides:

$4x - 3x + 12 = -48$

Simplifying:

$x + 12 = -48$

Step 3: Solve for $x$.

Subtract 12 from both sides:

$x = -48 - 12$

$x = -60$

Final Answer:

$x = -60$

Would you like more details, or do you have any questions?

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Here are 5 related questions for practice:

1. Solve $\frac{2}{3}x + 5 = \frac{4}{5}x - 3$.
2. What is the solution to $5x - 7 = 3x + 11$?
3. Solve $\frac{1}{4}x + 1 = \frac{1}{2}x - 3$.
4. How would you solve $6x + 8 = 4x - 12$?
5. Solve $\frac{3}{5}x + \frac{2}{5} = \frac{7}{10}x - 4$.

Tip: When solving equations with fractions, multiplying through by the least common denominator helps to eliminate the fractions early in the process!