## Solving the Equation: 0.6(x+7) = 0.5(x-3) + 6.8

This article will guide you through the steps to solve the linear equation 0.6(x+7) = 0.5(x-3) + 6.8. Let's break down the process:

### Step 1: Distribute

Start by distributing the constants on both sides of the equation:

**Left Side:**0.6 * (x + 7) = 0.6x + 4.2**Right Side:**0.5 * (x - 3) + 6.8 = 0.5x - 1.5 + 6.8

Now, the equation looks like this: 0.6x + 4.2 = 0.5x + 5.3

### Step 2: Combine Like Terms

Move all the 'x' terms to one side and the constant terms to the other side:

- Subtract 0.5x from both sides: 0.1x + 4.2 = 5.3
- Subtract 4.2 from both sides: 0.1x = 1.1

### Step 3: Isolate x

To isolate 'x', divide both sides by 0.1:

- 0.1x / 0.1 = 1.1 / 0.1
**x = 11**

### Solution

Therefore, the solution to the equation 0.6(x+7) = 0.5(x-3) + 6.8 is **x = 11**.