The given equation is:

$7(x - 3) = 4(x + 5)$

Let's solve for $x$:

1. Expand both sides: $7(x - 3) = 7x - 21$ $4(x + 5) = 4x + 20$ So, the equation becomes: $7x - 21 = 4x + 20$

2. Move all terms involving $x$ to one side: Subtract $4x$ from both sides: $7x - 4x - 21 = 20$ This simplifies to: $3x - 21 = 20$

3. Isolate $x$: Add 21 to both sides: $3x = 20 + 21$ $3x = 41$

4. Solve for $x$: Divide both sides by 3: $x = \frac{41}{3}$

Thus, the solution is $x = \frac{41}{3}$ or approximately $x \approx 13.67$.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How do you check if $x = \frac{41}{3}$ is the correct solution?
2. Can equations like this one have more than one solution?
3. How can you graphically represent this linear equation?
4. What is the process to solve for $x$ if both sides contain fractions?
5. How would this method change if the equation involved exponents or square roots?

Tip: Always simplify each step before moving to the next to avoid errors in complex equations.