The problem asks to solve the linear equation $3(x - 7) = 4 - 2(x + 2)$ for $x$.

1. Problem Description

The problem asks to solve the linear equation $3(x - 7) = 4 - 2(x + 2)$ for $x$.

2. Solution Steps

First, we distribute the numbers outside the parentheses into the parentheses on both sides of the equation:

$3(x - 7) = 3x - 21$

$-2(x + 2) = -2x - 4$

So the equation becomes:

$3x - 21 = 4 - 2x - 4$

Next, simplify the right side:

$3x - 21 = -2x$

Now, we want to isolate the $x$ terms on one side of the equation. Add $2x$ to both sides:

$3x + 2x - 21 = -2x + 2x$

$5x - 21 = 0$

Add 21 to both sides:

$5x - 21 + 21 = 0 + 21$

$5x = 21$

Finally, divide both sides by 5 to solve for $x$:

$\frac{5x}{5} = \frac{21}{5}$

$x = \frac{21}{5}$

3. Final Answer

$x = \frac{21}{5}$