Let's solve the equation step by step:

\[
\frac{4}{5}b - 3 = -\frac{1}{2}\left(\frac{3}{5}b + 4\right)
\]

### Step 1: Distribute the \(-\frac{1}{2}\) on the right side:
\[
\frac{4}{5}b - 3 = -\frac{1}{2} \cdot \frac{3}{5}b - \frac{1}{2} \cdot 4
\]
\[
\frac{4}{5}b - 3 = -\frac{3}{10}b - 2
\]

### Step 2: Get all the \(b\)-terms on one side by adding \(\frac{3}{10}b\) to both sides:
\[
\frac{4}{5}b + \frac{3}{10}b - 3 = -2
\]

### Step 3: Find a common denominator to add the fractions:
\[
\frac{8}{10}b + \frac{3}{10}b - 3 = -2
\]
\[
\frac{11}{10}b - 3 = -2
\]

### Step 4: Add 3 to both sides to isolate the term with \(b\):
\[
\frac{11}{10}b = 1
\]

### Step 5: Multiply both sides by \(\frac{10}{11}\) to solve for \(b\):
\[
b = \frac{10}{11}
\]

So, the solution is:
\[
\boxed{b = \frac{10}{11}}
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you solve equations involving fractions?
2. What is the method to find a common denominator?
3. How can you check if a solution to an equation is correct?
4. How do you solve an equation with variables on both sides?
5. What are some real-life applications of solving linear equations?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 4/5b - 3 = -1/2(3/5b + 4) step-by-step with a detailed solution. This problem involves solving equations with fractions and applying the distributive property. Suitable for students in Grades 7-9.

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