If `(0.3 (3x -4))/(5) + (0.4 x + 3.6)/(2) = 3.5x` then x = ____

Options

A. `0.1`
B. `0.3`
C. `0.5`
D. `0.2`

Explanation

To solve the equation \(\frac{0.3(3x - 4)}{5} + \frac{0.4x + 3.6}{2} = 3.5x\), we will follow these steps:

### Step 1: Eliminate the denominators
To eliminate the denominators, we will multiply the entire equation by the least common multiple (LCM) of the denominators, which is 10.

\[ 10 \left(\frac{0.3(3x - 4)}{5}\right) + 10 \left(\frac{0.4x + 3.6}{2}\right) = 10(3.5x) \]

### Step 2: Simplify the equation
Now, we simplify each term:

\[ 2 \cdot 0.3(3x - 4) + 5(0.4x + 3.6) = 35x \]

Calculating each term:

- \(2 \cdot 0.3(3x - 4) = 0.6(3x - 4) = 1.8x - 2.4\)
- \(5(0.4x + 3.6) = 2x + 18\)

So, the equation becomes:

\[ 1.8x - 2.4 + 2x + 18 = 35x \]

### Step 3: Combine like terms
Combine the \(x\) terms and the constant terms on the left side:

\[ (1.8x + 2x) + (-2.4 + 18) = 35x \]

This simplifies to:

\[ 3.8x + 15.6 = 35x \]

### Step 4: Isolate \(x\)
Now, we will isolate \(x\) by moving all \(x\) terms to one side and constant terms to the other side:

\[ 15.6 = 35x - 3.8x \]

This simplifies to:

\[ 15.6 = 31.2x \]

### Step 5: Solve for \(x\)
Now, divide both sides by 31.2 to find \(x\):

\[ x = \frac{15.6}{31.2} \]

Calculating this gives:

\[ x = 0.5 \]

### Final Answer:
Thus, the value of \(x\) is \(0.5\).

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