Solve : `3x + 2 (x+2) = 20 - (2x -5)`

Answer

To solve the equation \(3x + 2(x + 2) = 20 - (2x - 5)\), follow these steps:

### Step 1: Distribute the terms
Distribute \(2\) in \(2(x + 2)\) and \(-1\) in \(-(2x - 5)\).

\[ 2(x + 2) = 2x + 4 \]
\[ -(2x - 5) = -2x + 5 \]

Now, rewrite the equation:

\[ 3x + 2x + 4 = 20 - 2x + 5 \]

### Step 2: Simplify both sides
Combine like terms on both sides of the equation.

On the left side:
\[ 3x + 2x + 4 = 5x + 4 \]

On the right side:
\[ 20 + 5 - 2x = 25 - 2x \]

So, the equation now looks like:
\[ 5x + 4 = 25 - 2x \]

### Step 3: Move all terms involving \(x\) to one side
Add \(2x\) to both sides to move the \(x\) terms to the left side:

\[ 5x + 2x + 4 = 25 \]

This simplifies to:
\[ 7x + 4 = 25 \]

### Step 4: Move constant terms to the other side
Subtract \(4\) from both sides:

\[ 7x = 25 - 4 \]

This simplifies to:
\[ 7x = 21 \]

### Step 5: Solve for \(x\)
Divide both sides by \(7\):

\[ x = \frac{21}{7} \]

This simplifies to:
\[ x = 3 \]

### Final Answer
The solution to the equation is:
\[ \boxed{3} \]

---