Let's solve the equation step by step:

Given equation:
\[
0.6(4 - 2x) = 20.5 - (3x + 10)
\]

### Step 1: Distribute the \(0.6\) on the left side
\[
0.6 \cdot 4 - 0.6 \cdot 2x = 20.5 - (3x + 10)
\]
\[
2.4 - 1.2x = 20.5 - (3x + 10)
\]

### Step 2: Distribute the negative sign on the right side
\[
2.4 - 1.2x = 20.5 - 3x - 10
\]

### Step 3: Simplify the right side by combining like terms
\[
2.4 - 1.2x = (20.5 - 10) - 3x
\]
\[
2.4 - 1.2x = 10.5 - 3x
\]

### Step 4: Move all terms involving \(x\) to one side and constant terms to the other side
Add \(3x\) to both sides:
\[
2.4 - 1.2x + 3x = 10.5
\]
\[
2.4 + 1.8x = 10.5
\]

### Step 5: Isolate \(1.8x\)
Subtract \(2.4\) from both sides:
\[
1.8x = 10.5 - 2.4
\]
\[
1.8x = 8.1
\]

### Step 6: Solve for \(x\)
Divide both sides by \(1.8\):
\[
x = \frac{8.1}{1.8}
\]
\[
x = 4.5
\]

The solution is \(x = 4.5\).

Would you like further details on any of the steps? Here are some related questions:

1. How would the solution change if the coefficients were decimals or fractions?
2. What is the importance of distributing negative signs in equations?
3. How can you verify if \(x = 4.5\) is correct?
4. How do you solve an equation where variables appear on both sides?
5. What techniques can simplify equations before solving them?

**Tip:** Always simplify both sides of the equation as much as possible before solving for the variable.

Learn how to solve the equation 0.6(4 - 2x) = 20.5 - (3x + 10) step-by-step. This problem covers solving linear equations with the distributive property. Suitable for students in Grades 7-9.

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