## Solving the Equation: 0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8

This article will guide you through the process of solving the equation **0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8**.

### Step 1: Distribute

Begin by distributing the constants outside the parentheses:

- 0.5 * x = 0.5x
- 0.5 * 1.6 = 0.8
- 1.4 * 3x = 4.2x
- 1.4 * 2.4 = 3.36

Now the equation becomes:

**0.5x + 0.8 + 4.2x + 3.36 = 9.8**

### Step 2: Combine Like Terms

Combine the 'x' terms and the constant terms on the left side of the equation:

- 0.5x + 4.2x = 4.7x
- 0.8 + 3.36 = 4.16

The equation now looks like this:

**4.7x + 4.16 = 9.8**

### Step 3: Isolate the Variable

To isolate the 'x' term, subtract 4.16 from both sides of the equation:

**4.7x + 4.16 - 4.16 = 9.8 - 4.16**

This simplifies to:

**4.7x = 5.64**

### Step 4: Solve for x

Finally, divide both sides of the equation by 4.7 to solve for 'x':

**4.7x / 4.7 = 5.64 / 4.7**

This gives us:

**x = 1.2**

### Conclusion

Therefore, the solution to the equation **0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8** is **x = 1.2**.