## Solving the Equation: 0.6(x - 2) + 4.6 = 0.4(7 + x)

This article will guide you through the process of solving the equation **0.6(x - 2) + 4.6 = 0.4(7 + x)** step by step.

### 1. Distribute

First, we distribute the constants on both sides of the equation:

**0.6(x - 2)**becomes**0.6x - 1.2****0.4(7 + x)**becomes**2.8 + 0.4x**

This gives us the equation: **0.6x - 1.2 + 4.6 = 2.8 + 0.4x**

### 2. Combine Like Terms

Next, we combine the constant terms on each side of the equation:

**-1.2 + 4.6 = 3.4**

The equation now becomes: **0.6x + 3.4 = 2.8 + 0.4x**

### 3. Isolate the x Term

Now, we want to get all the x terms on one side of the equation and the constant terms on the other side.

- Subtract
**0.4x**from both sides:**0.6x + 3.4 - 0.4x = 2.8 + 0.4x - 0.4x** - This simplifies to:
**0.2x + 3.4 = 2.8**

### 4. Solve for x

Finally, we isolate the **x** term by subtracting **3.4** from both sides:

**0.2x + 3.4 - 3.4 = 2.8 - 3.4**- This gives us
**0.2x = -0.6**

Now, divide both sides by **0.2** to solve for **x**:

**0.2x / 0.2 = -0.6 / 0.2**- This results in
**x = -3**

### Conclusion

Therefore, the solution to the equation **0.6(x - 2) + 4.6 = 0.4(7 + x)** is **x = -3**.