Solve:`x-(2x-(3x-4)/7)=(4x-27)/3-3`.

Options

A. 2
B. 4
C. 3
D. 6

Answer

To solve the equation \( x - \left( 2x - \frac{(3x - 4)}{7} \right) = \frac{(4x - 27)}{3} - 3 \), we will follow these steps:

### Step 1: Simplify the left side of the equation

Start with the left side:

\[ x - \left( 2x - \frac{(3x - 4)}{7} \right) \]

Distributing the negative sign inside the parentheses:

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

Combine like terms:

\[ -x + \frac{(3x - 4)}{7} \]

### Step 2: Simplify the right side of the equation

Now, simplify the right side:

\[ \frac{(4x - 27)}{3} - 3 \]

Convert \(3\) to a fraction with a denominator of \(3\):

\[ \frac{(4x - 27)}{3} - \frac{9}{3} \]

Combine the fractions:

\[ \frac{(4x - 27 - 9)}{3} = \frac{(4x - 36)}{3} \]

### Step 3: Set the simplified sides equal to each other

Now we have:

\[ -x + \frac{(3x - 4)}{7} = \frac{(4x - 36)}{3} \]

### Step 4: Eliminate the fractions

To eliminate the fractions, find the least common multiple (LCM) of the denominators \(7\) and \(3\), which is \(21\). Multiply both sides by \(21\):

\[ 21 \left( -x + \frac{(3x - 4)}{7} \right) = 21 \left( \frac{(4x - 36)}{3} \right) \]

This simplifies to:

\[ -21x + 3(3x - 4) = 7(4x - 36) \]

Distributing on both sides:

\[ -21x + 9x - 12 = 28x - 252 \]

### Step 5: Combine like terms

Combine like terms on the left side:

\[ -12x - 12 = 28x - 252 \]

### Step 6: Move all terms involving \(x\) to one side

Add \(12x\) to both sides:

\[ -12 = 28x + 12x - 252 \]

Combine like terms:

\[ -12 = 40x - 252 \]

### Step 7: Isolate \(x\)

Add \(252\) to both sides:

\[ 240 = 40x \]

Now, divide by \(40\):

\[ x = \frac{240}{40} = 6 \]

### Final Solution

Thus, the solution to the equation is:

\[ \boxed{6} \]

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