To solve the equation $3(x - 4) + 2(x + 5) = 4(x + 3)$ algebraically, follow these steps:

Step 1: Expand both sides of the equation.

Distribute the numbers outside the parentheses:

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

Now the equation becomes: $3x - 12 + 2x + 10 = 4x + 12$

Step 2: Combine like terms.

On the left side, combine the terms involving $x$ and the constant terms:

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

Step 3: Move all terms involving $x$ to one side.

Subtract $4x$ from both sides to isolate $x$ on one side:

$5x - 4x - 2 = 12$ $x - 2 = 12$

Step 4: Solve for $x$.

Add 2 to both sides:

$x = 12 + 2$ $x = 14$

So, the solution is $x = 14$.

Summary:

The solution to the equation is $x = 14$.

---

Would you like a detailed explanation of any particular step, or do you have any questions?

Here are 5 related questions you could explore:

1. What is the process for solving equations with variables on both sides?
2. How do you handle equations with fractions or decimals?
3. What is the difference between linear and quadratic equations?
4. How do you solve an equation with multiple variables?
5. What are the steps for checking if your solution is correct?

Tip: After solving any equation, it's always good practice to plug your solution back into the original equation to verify it.