The equation is:

\[
a \cdot (5 - x) = bx - 8
\]

To solve for \( x \), let's expand both sides and isolate \( x \):

1. Distribute \( a \) on the left side:
   \[
   a \cdot (5 - x) = 5a - ax
   \]
   So, the equation becomes:
   \[
   5a - ax = bx - 8
   \]

2. Move all terms involving \( x \) to one side and constant terms to the other:
   \[
   -ax - bx = -5a - 8
   \]

3. Factor out \( x \) on the left side:
   \[
   x(-a - b) = -5a - 8
   \]

4. Finally, solve for \( x \) by dividing both sides by \( -a - b \):
   \[
   x = \frac{-5a - 8}{-a - b}
   \]

You can simplify further if needed, but this is the general solution for \( x \).

Would you like more details on this solution, or do you have any questions?

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Here are 5 related questions to explore further:

1. What happens to the solution if \( a = b \)?
2. How does the solution change if \( a \) or \( b \) are negative?
3. Can we solve for \( a \) in terms of \( x \) and \( b \)?
4. How would the equation look if an additional constant is added to both sides?
5. How can you check if a particular \( x \) satisfies the original equation?

**Tip:** When solving for variables, remember to always check for cases where the denominator might be zero.

Explore how to solve the linear equation a(5 - x) = bx - 8 step-by-step. This solution involves key algebraic concepts such as distribution, moving variables, and solving for x. Learn how to apply the distributive property and properties of equality, suitable for Grades 8-10.

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