Solve for `x : 2(2-3x) - (4 + x) = 7`

Answer

To solve the equation \( 2(2 - 3x) - (4 + x) = 7 \), we will follow these steps:

### Step 1: Distribute the terms
Start by distributing the \(2\) in the first term and the negative sign in the second term.

\[ 2(2 - 3x) - (4 + x) = 7 \]

Distributing gives:

\[ 4 - 6x - 4 - x = 7 \]

### Step 2: Combine like terms
Now, combine the like terms on the left side of the equation.

\[ (4 - 4) + (-6x - x) = 7 \]

This simplifies to:

\[ 0 - 7x = 7 \]

or simply:

\[ -7x = 7 \]

### Step 3: Solve for \(x\)
Now, divide both sides of the equation by \(-7\) to isolate \(x\).

\[ x = \frac{7}{-7} \]

This simplifies to:

\[ x = -1 \]

### Final Answer
The solution to the equation is:

\[ x = -1 \]

---