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.

Learn how to solve the linear equation ax + b = cx + d with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and solving equations by isolating variables. Suitable for students in Grades 7-9.

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