## Solving the Linear Equation: 0.4(x-9) - 0.3(x+2) = 0.7

This article will guide you through the steps to solve the linear equation 0.4(x-9) - 0.3(x+2) = 0.7.

### Step 1: Distribute

Begin by distributing the constants outside the parentheses:

- 0.4(x-9) = 0.4x - 3.6
- 0.3(x+2) = 0.3x + 0.6

Now the equation looks like this: 0.4x - 3.6 - 0.3x - 0.6 = 0.7

### Step 2: Combine Like Terms

Combine the 'x' terms and the constant terms:

- (0.4x - 0.3x) + (-3.6 - 0.6) = 0.7
- 0.1x - 4.2 = 0.7

### Step 3: Isolate the 'x' Term

Add 4.2 to both sides of the equation:

- 0.1x - 4.2 + 4.2 = 0.7 + 4.2
- 0.1x = 4.9

### Step 4: Solve for 'x'

Divide both sides by 0.1 to isolate 'x':

- 0.1x / 0.1 = 4.9 / 0.1
**x = 49**

### Conclusion

Therefore, the solution to the linear equation 0.4(x-9) - 0.3(x+2) = 0.7 is **x = 49**.