The problem is to solve the linear equation $7 - 2x = -5$ for the variable $x$.

1. Problem Description

The problem is to solve the linear equation $7 - 2x = -5$ for the variable $x$.

2. Solution Steps

We need to isolate $x$ on one side of the equation.

First, subtract 7 from both sides of the equation:

$7 - 2x - 7 = -5 - 7$

$-2x = -12$

Next, divide both sides by -2:

$\frac{-2x}{-2} = \frac{-12}{-2}$

$x = 6$

3. Final Answer

The solution to the equation $7 - 2x = -5$ is $x = 6$.