The given equation is:

$ax + b = cx + d$

To solve for $x$, let's follow these steps:

1. Move all terms involving $x$ to one side: Subtract $cx$ from both sides to eliminate it from the right-hand side: $ax - cx + b = d$ Simplify: $(a - c)x + b = d$

2. Move constant terms to the other side: Subtract $b$ from both sides: $(a - c)x = d - b$

3. Solve for $x$: Divide both sides by $a - c$, assuming $a \neq c$: $x = \frac{d - b}{a - c}$

So, the solution for $x$ is:

$x = \frac{d - b}{a - c}$

Would you like a more detailed explanation of any of the steps?

Here are 5 related questions to explore:

1. What happens if $a = c$? How does it affect the equation?
2. How can you solve a system of equations with multiple linear equations like this?
3. How does this solution change if we add coefficients or higher powers of $x$?
4. How does the solution change if instead of linear terms, there are quadratic terms like $ax^2$?
5. Can this equation have no solutions? If yes, under what conditions?

Tip: Always simplify the equation step-by-step, isolating $x$ or the variable of interest, which helps avoid mistakes in solving.