To solve the equation \( 4 = \frac{3}{-4x} + b \), we'll need to isolate \( b \).

### Step 1: Simplify the equation.
Move \( \frac{3}{-4x} \) to the other side of the equation:
\[
b = 4 - \frac{3}{-4x}
\]
This simplifies to:
\[
b = 4 + \frac{3}{4x}
\]

Thus, the expression for \( b \) in terms of \( x \) is:
\[
b = 4 + \frac{3}{4x}
\]

Would you like to see more details or have any questions?

Here are 5 related questions to explore further:

1. How do we solve for \( x \) if \( b \) is known?
2. What happens if \( x = 0 \) in this equation?
3. Can you rewrite the equation in terms of \( x \) instead of \( b \)?
4. How does the equation change if you multiply both sides by \( x \)?
5. What is the geometric interpretation of this equation?

**Tip:** Always watch out for division by zero, which can make equations undefined.

Learn how to solve the equation 4 = 3 / -4x + b by isolating the variable b. This problem involves concepts of algebra and fractions and provides a step-by-step solution suitable for students in Grades 8-10.

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