Let's solve the equation \( 0.6(4 - 2x) = 20.5 - (3x + 10) \).

### Step 1: Distribute the 0.6 on the left-hand side and simplify both sides.
\[
0.6 \times 4 - 0.6 \times 2x = 20.5 - (3x + 10)
\]
\[
2.4 - 1.2x = 20.5 - 3x - 10
\]

### Step 2: Simplify the right-hand side.
\[
2.4 - 1.2x = 20.5 - 10 - 3x
\]
\[
2.4 - 1.2x = 10.5 - 3x
\]

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

### Step 4: Isolate \(x\).
Subtract 2.4 from both sides:
\[
1.8x = 10.5 - 2.4
\]
\[
1.8x = 8.1
\]

### Step 5: Solve for \(x\).
\[
x = \frac{8.1}{1.8} = 4.5
\]

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

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. Solve \( 0.7(3 - 4x) = 18 - (2x + 7) \).
2. Simplify and solve \( 5(2x - 1) = 3x + 4 \).
3. Solve \( 0.5(6x + 8) = 2(5x - 3) \).
4. Solve the system of equations: \( 2x + 3y = 12 \) and \( 4x - y = 5 \).
5. Solve \( 3(x + 4) - 2x = 5x + 12 \).

**Tip:** When solving equations, always distribute terms and simplify each side before moving variables to one side!

Discover how to solve the linear equation 0.6(4 - 2x) = 20.5 - (3x + 10) using distribution, simplification, and variable isolation techniques. This step-by-step guide is perfect for students in Grades 8-10 looking to strengthen their algebra skills.

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