Let's solve the equation $3x - 5 - 2(-x + 9) = 2$.

Step 1: Distribute the -2 on the left-hand side

$3x - 5 - 2(-x + 9) = 3x - 5 + 2x - 18 = 2$ This simplifies to: $5x - 23 = 2$

Step 2: Add 23 to both sides to isolate the term with $x$

$5x - 23 + 23 = 2 + 23$ $5x = 25$

Step 3: Divide by 5 to solve for $x$

$x = \frac{25}{5} = 5$

Thus, the solution is $x = 5$.

Would you like further details or have any questions?

Here are five related problems for practice:

1. Solve $4x - 7 - 3(x - 4) = 5$.
2. Solve $2x - 5 + 4(2 - x) = 6$.
3. Solve $5x - 2(3x - 5) = 12$.
4. Solve $3(x + 2) - 4(x - 1) = 0$.
5. Solve $2(x - 3) - (x + 4) = 10$.

Tip: Always distribute terms carefully when solving equations to avoid errors in simplifying.