The solution of 0.2 (2x - 1)-0.5 (3x – 1) = 0.4 is

Options

A. `(1)/(11)`
B. `-(1)/(11)`
C. `(3)/(11)`
D. `-(3)/(11)`

Answer

To solve the equation \(0.2 (2x - 1) - 0.5 (3x - 1) = 0.4\), we will follow these steps:

### Step 1: Convert Decimals to Fractions
First, we convert the decimals into fractions:
- \(0.2 = \frac{2}{10} = \frac{1}{5}\)
- \(0.5 = \frac{5}{10} = \frac{1}{2}\)
- \(0.4 = \frac{4}{10} = \frac{2}{5}\)

So, we rewrite the equation as:
\[ \frac{1}{5}(2x - 1) - \frac{1}{2}(3x - 1) = \frac{2}{5} \]

### Step 2: Eliminate Fractions
To eliminate the fractions, we can multiply the entire equation by 10 (the least common multiple of 5 and 2):
\[ 10 \left(\frac{1}{5}(2x - 1)\right) - 10 \left(\frac{1}{2}(3x - 1)\right) = 10 \left(\frac{2}{5}\right) \]
This simplifies to:
\[ 2(2x - 1) - 5(3x - 1) = 4 \]

### Step 3: Distribute
Now, distribute the terms:
\[ 4x - 2 - 15x + 5 = 4 \]

### Step 4: Combine Like Terms
Combine the \(x\) terms and the constant terms:
\[ (4x - 15x) + (-2 + 5) = 4 \]
This simplifies to:
\[ -11x + 3 = 4 \]

### Step 5: Isolate the Variable
Now, isolate \(x\) by moving the constant term to the other side:
\[ -11x = 4 - 3 \]
This simplifies to:
\[ -11x = 1 \]

### Step 6: Solve for \(x\)
Finally, divide both sides by -11:
\[ x = -\frac{1}{11} \]

### Final Solution
Thus, the solution of the equation is:
\[ x = -\frac{1}{11} \]

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