We are asked to solve the linear equation $x - 15 = x + 2x + 1$ for $x$.

1. Problem Description

We are asked to solve the linear equation $x - 15 = x + 2x + 1$ for $x$.

2. Solution Steps

First, combine like terms on the right side of the equation:

$x - 15 = 3x + 1$

Next, subtract $x$ from both sides of the equation to group the x terms on the right:

$x - 15 - x = 3x + 1 - x$

$-15 = 2x + 1$

Then, subtract 1 from both sides of the equation to isolate the term with x:

$-15 - 1 = 2x + 1 - 1$

$-16 = 2x$

Finally, divide both sides of the equation by 2 to solve for x:

$\frac{-16}{2} = \frac{2x}{2}$

$-8 = x$

3. Final Answer

$x = -8$