Solve :
`(x+2)/(6)-((11-x)/(3)-(1)/(4))=(3x-4)/(12)`

Options

A. `19`
B. `11`
C. `17`
D. `10`

Answer

To solve the equation

\[ \frac{x+2}{6} - \left(\frac{11-x}{3} - \frac{1}{4}\right) = \frac{3x-4}{12} \]

we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 6, 3, 4, and 12. The least common multiple (LCM) of these numbers is 12. We will multiply each term by 12 to eliminate the fractions.

### Step 2: Multiply through by 12
Multiplying each term by 12 gives us:

\[ 12 \cdot \frac{x+2}{6} - 12 \cdot \left(\frac{11-x}{3} - \frac{1}{4}\right) = 12 \cdot \frac{3x-4}{12} \]

This simplifies to:

\[ 2(x+2) - 4(11-x) + 3 = 3x - 4 \]

### Step 3: Distribute and simplify
Now we will distribute the terms:

\[ 2x + 4 - 44 + 4x + 3 = 3x - 4 \]

Combining like terms on the left side:

\[ (2x + 4x) + (4 - 44 + 3) = 3x - 4 \]

This simplifies to:

\[ 6x - 37 = 3x - 4 \]

### Step 4: Move all terms involving x to one side
Now, we will move \(3x\) to the left side by subtracting \(3x\) from both sides:

\[ 6x - 3x - 37 = -4 \]

This simplifies to:

\[ 3x - 37 = -4 \]

### Step 5: Move constant terms to the other side
Next, we will add 37 to both sides:

\[ 3x = -4 + 37 \]

This gives us:

\[ 3x = 33 \]

### Step 6: Solve for x
Finally, we divide both sides by 3 to solve for \(x\):

\[ x = \frac{33}{3} = 11 \]

Thus, the solution to the equation is:

\[ \boxed{11} \]

---