Let's solve the equation $4 = -\frac{3}{4}(-14) + b$ for $b$.

Step 1: Simplify the expression on the right side

First, calculate $-\frac{3}{4} \times (-14)$: $-\frac{3}{4} \times (-14) = \frac{3}{4} \times 14 = \frac{42}{4} = 10.5$

Step 2: Substitute back into the equation

$4 = 10.5 + b$

Step 3: Solve for $b$

Subtract 10.5 from both sides: $b = 4 - 10.5$ $b = -6.5$

Final Answer:

$b = -6.5$

Would you like a detailed explanation of any step or have any questions?

Here are 5 related questions to explore:

1. How do you solve an equation involving fractions?
2. What is the process for solving equations with variables on both sides?
3. How can you check if your solution for $b$ is correct?
4. How do you simplify expressions involving multiple negative signs?
5. What are some real-life applications of solving linear equations?

Tip: When dealing with fractions, it's often helpful to simplify them step by step to avoid mistakes.