https://file.aiquickdraw.com/mathbot/file/17268479228112dz671ws.jpg

The equation provided in the image is:

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

We need to solve for \( x \). Here's the step-by-step solution:

### Step 1: Distribute \( a \) on the left-hand side.
\[
a(5 - x) = a \cdot 5 - a \cdot x = 5a - ax
\]

Now the equation becomes:
\[
5a - ax = bx - 8
\]

### Step 2: Move all terms involving \( x \) to one side and constants to the other side.
To do this, add \( ax \) to both sides and add \( 8 \) to both sides:
\[
5a + 8 = bx + ax
\]

### Step 3: Factor out \( x \) on the right-hand side.
\[
5a + 8 = x(b + a)
\]

### Step 4: Solve for \( x \).
\[
x = \frac{5a + 8}{b + a}
\]

This is the solution for \( x \) assuming \( b + a \neq 0 \), since division by zero is undefined.

Would you like more details on this solution? Here are 5 related questions to explore this topic further:

1. How does the distributive property work in equations?
2. What happens if \( b + a = 0 \)? How do we handle such cases?
3. How can you check if this solution satisfies the original equation?
4. What are some other methods to solve linear equations involving variables on both sides?
5. How would the equation change if there were additional constants involved?

**Tip:** Always ensure that terms involving the unknown variable are grouped together on one side before solving.

Learn how to solve the linear equation a(5 - x) = bx - 8 with a step-by-step solution. This problem covers key algebraic concepts, including the distributive property, grouping variables, and solving for x. Suitable for high school students in Grades 9-11.

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