We are asked to find the value of $x$ that satisfies the equation $7 + 5(x - 3) = 22$.

1. Problem Description

We are asked to find the value of $x$ that satisfies the equation $7 + 5(x - 3) = 22$.

2. Solution Steps

First, subtract 7 from both sides of the equation:

$7 + 5(x - 3) - 7 = 22 - 7$

$5(x - 3) = 15$

Next, divide both sides by 5:

$\frac{5(x - 3)}{5} = \frac{15}{5}$

$x - 3 = 3$

Finally, add 3 to both sides:

$x - 3 + 3 = 3 + 3$

$x = 6$

3. Final Answer

$x = 6$