Solve the following equations :
`3(x+1)=12+4(x-1)`

Answer

To solve the equation \( 3(x+1) = 12 + 4(x-1) \), we will follow these steps:

### Step 1: Expand both sides of the equation
We will distribute the numbers outside the parentheses on both sides.

\[ 3(x + 1) = 12 + 4(x - 1) \]

Expanding the left-hand side (LHS):
\[ 3 \cdot x + 3 \cdot 1 = 3x + 3 \]

Expanding the right-hand side (RHS):
\[ 12 + 4 \cdot x - 4 \cdot 1 = 12 + 4x - 4 = 4x + 8 \]

So, the equation now looks like:
\[ 3x + 3 = 4x + 8 \]

### Step 2: Rearrange the equation
Next, we will move all the terms involving \( x \) to one side and the constant terms to the other side.

Subtract \( 3x \) from both sides:
\[ 3 = 4x - 3x + 8 \]
This simplifies to:
\[ 3 = x + 8 \]

### Step 3: Isolate \( x \)
Now, we will isolate \( x \) by subtracting 8 from both sides:
\[ 3 - 8 = x \]
This simplifies to:
\[ -5 = x \]

### Conclusion
Thus, the solution to the equation is:
\[ x = -5 \]

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