We need to solve the following linear equation for $x$: $3x + 7 - 11x = 31$

1. Problem Description

We need to solve the following linear equation for $x$:

$3x + 7 - 11x = 31$

2. Solution Steps

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

$3x - 11x + 7 = 31$

$-8x + 7 = 31$

Next, subtract 7 from both sides of the equation:

$-8x + 7 - 7 = 31 - 7$

$-8x = 24$

Finally, divide both sides of the equation by -8:

$\frac{-8x}{-8} = \frac{24}{-8}$

$x = -3$

3. Final Answer

$x = -3$