To solve the equation:

\[
ax + 3x = bx + 5
\]

We start by simplifying and isolating terms involving \(x\).

1. Combine like terms on the left-hand side:
   \[
   (a + 3)x = bx + 5
   \]

2. Move all terms involving \(x\) to one side:
   \[
   (a + 3)x - bx = 5
   \]

3. Factor out \(x\) on the left-hand side:
   \[
   (a + 3 - b)x = 5
   \]

4. Solve for \(x\) by dividing both sides by \((a + 3 - b)\) (assuming \(a + 3 - b \neq 0\)):
   \[
   x = \frac{5}{a + 3 - b}
   \]

Thus, the solution is:

\[
x = \frac{5}{a + 3 - b}
\]

Would you like further details, or do you have any questions about this solution?

Here are some related questions:
1. What happens if \(a + 3 - b = 0\)?
2. How would the solution change if \(a = b\)?
3. Can this equation be solved graphically? How would it look?
4. How does this equation relate to solving linear equations generally?
5. How can we check if the solution \(x = \frac{5}{a + 3 - b}\) is valid?

**Tip:** Always check if the denominator is non-zero when solving equations of this form!

Learn how to solve the linear equation ax + 3x = bx + 5 with a detailed step-by-step solution. This problem focuses on simplifying linear expressions and solving for x using algebraic techniques. Suitable for students in Grades 8-10.

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