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## Solving the equation 0.5(x-0.4)/3.5 - 0.6(x-2.7)/4.2 = x+6.1

This article will guide you through the steps on how to solve the equation:

**0.5(x-0.4)/3.5 - 0.6(x-2.7)/4.2 = x+6.1**

### Step 1: Simplify the fractions

**Multiply both sides of the equation by the least common multiple (LCM) of the denominators (3.5 and 4.2), which is 29.4.**This will eliminate the fractions.**Simplify the equation after multiplying:**

```
29.4 * [0.5(x-0.4)/3.5 - 0.6(x-2.7)/4.2] = 29.4 * (x+6.1)
4.2(x-0.4) - 4.2(x-2.7) = 29.4x + 179.94
```

### Step 2: Distribute and combine like terms

**Distribute the 4.2 on the left side of the equation:**

```
4.2x - 1.68 - 4.2x + 11.34 = 29.4x + 179.94
```

**Combine like terms on the left side:**

```
9.66 = 29.4x + 179.94
```

### Step 3: Isolate the variable

**Subtract 179.94 from both sides:**

```
9.66 - 179.94 = 29.4x
-170.28 = 29.4x
```

### Step 4: Solve for x

**Divide both sides by 29.4:**

```
-170.28 / 29.4 = x
x = -5.79
```

### Solution

Therefore, the solution to the equation **0.5(x-0.4)/3.5 - 0.6(x-2.7)/4.2 = x+6.1** is **x = -5.79**.