Solve for X: 18.5 - (3/9)x + (4/9)x = 13.5 Linear Equation

To solve this problem, we'll follow these steps:

• Step 1: Combine like terms.

• Step 2: Simplify and solve for $x$.

• Step 3: Verify the solution against provided choices.

Now, let's work through each step:

Step 1: Combine like terms on the left side of the equation.
The equation is: $18.5 - \frac{3}{9}x + \frac{4}{9}x = 9.7 + 3.8$.

Combine the $x$-terms: $\frac{4}{9}x - \frac{3}{9}x = \frac{1}{9}x$.

The equation now looks like: $18.5 + \frac{1}{9}x = 9.7 + 3.8$.

Step 2: Simplify the right side of the equation.
Calculate $9.7 + 3.8 = 13.5$.
The simplified equation becomes $18.5 + \frac{1}{9}x = 13.5$.

Subtract 18.5 from both sides to isolate the $x$-term.
$\frac{1}{9}x = 13.5 - 18.5$.
$\frac{1}{9}x = -5$.

To solve for $x$, multiply both sides by 9 (the reciprocal of $\frac{1}{9}$):
$x = -5 \times 9$.

Therefore, the solution to the problem is $x = -45$.

Step 3: Verify the solution by comparing it with the given choices.

Since the correct answer $-45$ is the first choice on the provided list, our solution is verified.