We are given the equation:

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

### Step 1: Distribute the 0.6 on the left-hand side

\[
0.6 \times 4 - 0.6 \times 2x = 20.5 - (3x + 10)
\]

Simplifying this:

\[
2.4 - 1.2x = 20.5 - 3x - 10
\]

### Step 2: Simplify the right-hand side

\[
2.4 - 1.2x = 10.5 - 3x
\]

### Step 3: Combine like terms
Now let's move the \(x\)-terms to one side and the constants to the other side. Add \(3x\) to both sides:

\[
2.4 - 1.2x + 3x = 10.5
\]

This simplifies to:

\[
2.4 + 1.8x = 10.5
\]

### Step 4: Isolate \(x\)
Subtract 2.4 from both sides:

\[
1.8x = 10.5 - 2.4
\]

\[
1.8x = 8.1
\]

### Step 5: Solve for \(x\)
Divide both sides by 1.8:

\[
x = \frac{8.1}{1.8} = 4.5
\]

### Final Answer:
\[
x = 4.5
\]

Would you like further clarification or details on any step?

### 5 Related Questions:
1. How do you solve equations with parentheses and distributive property?
2. How do you combine like terms in algebraic expressions?
3. What are the methods for isolating variables in linear equations?
4. How do you handle equations with multiple steps involving fractions or decimals?
5. How can you verify solutions to algebraic equations?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies both sides!

This guide explains how to solve the linear equation 0.6(4 - 2x) = 20.5 - (3x + 10) using distributive property, combining like terms, and isolating the variable. Suitable for students in Grades 8-10, covering key algebraic concepts with step-by-step explanations.

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