x का मान ज्ञात करो - `(2)/(3)[4x-1] -[4x-(1-3x)/(2)]=(x-7)/(2)`

Options

A. 0
B. 1
C. 2
D. 5

Answer

To solve the equation

\[ \frac{2}{3}[4x-1] - [4x - \frac{(1-3x)}{2}] = \frac{(x-7)}{2} \]

we will follow these steps:

### Step 1: Simplify the left-hand side

First, we simplify the expression on the left-hand side.

The first term is:

\[ \frac{2}{3}(4x - 1) = \frac{8x - 2}{3} \]

The second term is:

\[ 4x - \frac{(1 - 3x)}{2} = 4x - \frac{1}{2} + \frac{3x}{2} = 4x + \frac{3x}{2} - \frac{1}{2} \]

To combine \(4x\) and \(\frac{3x}{2}\), we convert \(4x\) to have a common denominator:

\[ 4x = \frac{8x}{2} \]

Thus,

\[ 4x + \frac{3x}{2} = \frac{8x + 3x}{2} = \frac{11x}{2} \]

Now, substituting this back into the equation gives:

\[ \frac{8x - 2}{3} - \left(\frac{11x}{2} - \frac{1}{2}\right) = \frac{(x-7)}{2} \]

### Step 2: Combine the left-hand side

Now we rewrite the left-hand side:

\[ \frac{8x - 2}{3} - \frac{11x - 1}{2} \]

To combine these fractions, we need a common denominator, which is 6:

\[ \frac{8x - 2}{3} = \frac{2(8x - 2)}{6} = \frac{16x - 4}{6} \]

\[ \frac{11x - 1}{2} = \frac{3(11x - 1)}{6} = \frac{33x - 3}{6} \]

Now we can combine the fractions:

\[ \frac{16x - 4 - (33x - 3)}{6} = \frac{16x - 4 - 33x + 3}{6} = \frac{-17x - 1}{6} \]

### Step 3: Set the equation

Now we set the left-hand side equal to the right-hand side:

\[ \frac{-17x - 1}{6} = \frac{x - 7}{2} \]

### Step 4: Cross-multiply

Cross-multiplying gives:

\[ -17x - 1 = 3(x - 7) \]

### Step 5: Expand and simplify

Expanding the right-hand side:

\[ -17x - 1 = 3x - 21 \]

Now, we move all terms involving \(x\) to one side and constant terms to the other:

\[ -17x - 3x = -21 + 1 \]

This simplifies to:

\[ -20x = -20 \]

### Step 6: Solve for \(x\)

Dividing both sides by -20 gives:

\[ x = 1 \]

### Final Answer

Thus, the value of \(x\) is:

\[ \boxed{1} \]

---