The problem asks us to solve the linear equation $15 + x = 3x - 17$ for the variable $x$.

1. Problem Description

The problem asks us to solve the linear equation $15 + x = 3x - 17$ for the variable $x$.

2. Solution Steps

We are given the equation $15 + x = 3x - 17$.

First, we want to isolate the terms with $x$ on one side of the equation and the constant terms on the other side.

Subtract $x$ from both sides of the equation:

$15 + x - x = 3x - 17 - x$

$15 = 2x - 17$

Next, add 17 to both sides of the equation:

$15 + 17 = 2x - 17 + 17$

$32 = 2x$

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

$\frac{32}{2} = \frac{2x}{2}$

$16 = x$

3. Final Answer

The solution to the equation $15 + x = 3x - 17$ is $x = 16$.