Solve the equations and check your answer in the case:
`x-(2x-(3x-4)/(7))= (4x-27)/(3)-3`

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
We start with the left side:
\[ x - \left(2x - \frac{(3x - 4)}{7}\right) \]
Distributing the negative sign:
\[ x - 2x + \frac{(3x - 4)}{7} \]
This simplifies to:
\[ -x + \frac{(3x - 4)}{7} \]

### Step 2: Combine terms on the left side
To combine the terms, we need a common denominator. The common denominator is 7:
\[ -x = -\frac{7x}{7} \]
Thus, we rewrite the left side:
\[ -\frac{7x}{7} + \frac{(3x - 4)}{7} = \frac{-7x + 3x - 4}{7} = \frac{-4x - 4}{7} \]

### Step 3: Simplify the right side of the equation
Now we simplify the right side:
\[ \frac{(4x - 27)}{3} - 3 \]
Convert 3 to a fraction with a denominator of 3:
\[ 3 = \frac{9}{3} \]
So, we have:
\[ \frac{(4x - 27)}{3} - \frac{9}{3} = \frac{(4x - 27 - 9)}{3} = \frac{(4x - 36)}{3} \]

### Step 4: Set the two sides equal
Now we have:
\[ \frac{-4x - 4}{7} = \frac{(4x - 36)}{3} \]

### Step 5: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ -4x - 4) \cdot 3 = (4x - 36) \cdot 7 \]
This simplifies to:
\[ -12x - 12 = 28x - 252 \]

### Step 6: Rearrange the equation
Now, we will move all terms involving \(x\) to one side and constant terms to the other side:
\[ -12x - 28x = -252 + 12 \]
This simplifies to:
\[ -40x = -240 \]

### Step 7: Solve for \(x\)
Dividing both sides by -40:
\[ x = \frac{-240}{-40} = 6 \]

### Step 8: Check the solution
Substituting \(x = 6\) back into the original equation:
Left side:
\[ 6 - \left(2(6) - \frac{(3(6) - 4)}{7}\right) = 6 - \left(12 - \frac{18 - 4}{7}\right) = 6 - \left(12 - \frac{14}{7}\right) = 6 - \left(12 - 2\right) = 6 - 10 = -4 \]
Right side:
\[ \frac{(4(6) - 27)}{3} - 3 = \frac{(24 - 27)}{3} - 3 = \frac{-3}{3} - 3 = -1 - 3 = -4 \]
Both sides are equal, confirming our solution is correct.

### Final Answer:
\[ x = 6 \]