The given equation is:

$-3 + 4(x - 3) = -2(x - 5) + 5$

Let's solve this step by step.

Step 1: Expand both sides of the equation.

Distribute the constants across the terms inside the parentheses:

$-3 + 4(x - 3) = -2(x - 5) + 5$

$-3 + 4x - 12 = -2x + 10 + 5$

Simplify the constants:

$4x - 15 = -2x + 15$

Step 2: Move all terms involving $x$ to one side and constant terms to the other side.

Add $2x$ to both sides:

$4x + 2x - 15 = 15$

This simplifies to:

$6x - 15 = 15$

Step 3: Move the constant term to the other side.

Add 15 to both sides:

$6x = 30$

Step 4: Solve for $x$.

Divide both sides by 6:

$x = 5$

Solution:

The solution to the equation is $x = 5$.

Would you like any further details or have any questions?

Here are some related questions for practice:

1. Can you solve an equation similar to this, but with fractions?
2. How do we solve an equation with variables on both sides when there are decimals involved?
3. What happens if we encounter an equation that has no solution or infinitely many solutions?
4. How can we solve inequalities that involve a similar structure?
5. Can we apply the same steps if the equation involves square roots or exponents?

Tip: Always simplify both sides of an equation as much as possible before moving terms across the equality sign.