The problem is to solve the linear equation $x + 3(x + 1) = 2x$ for the variable $x$.

1. Problem Description

The problem is to solve the linear equation $x + 3(x + 1) = 2x$ for the variable $x$.

2. Solution Steps

We are given the equation $x + 3(x + 1) = 2x$.

First, we distribute the 3:

$x + 3x + 3 = 2x$

Combine like terms on the left side:

$4x + 3 = 2x$

Subtract $2x$ from both sides of the equation:

$4x - 2x + 3 = 2x - 2x$

$2x + 3 = 0$

Subtract 3 from both sides of the equation:

$2x + 3 - 3 = 0 - 3$

$2x = -3$

Divide both sides by 2:

$\frac{2x}{2} = \frac{-3}{2}$

$x = -\frac{3}{2}$

3. Final Answer

$x = -\frac{3}{2}$