https://file.aiquickdraw.com/mathbot/file/17254545737192bzro9wt.jpg

The image asks to solve the equation:

\[
bx - 3b + 6 = 0
\]

Let's solve this equation step by step.

### Step 1: Isolate the term involving \( x \)
First, subtract 6 from both sides to move the constant term:

\[
bx - 3b = -6
\]

### Step 2: Solve for \( x \)
Now, add \( 3b \) to both sides:

\[
bx = 3b - 6
\]

Finally, divide both sides by \( b \) (assuming \( b \neq 0 \)):

\[
x = \frac{3b - 6}{b}
\]

### Step 3: Simplify the expression
We can simplify this by dividing each term in the numerator by \( b \):

\[
x = 3 - \frac{6}{b}
\]

So the solution for \( x \) is:

\[
\boxed{x = 3 - \frac{6}{b}}
\]

Would you like further details on the steps or have any questions?

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**Related Questions:**

1. What happens to the value of \( x \) as \( b \) approaches zero?
2. How would the solution change if the equation had an additional constant term on the right side?
3. Can you graph the relationship between \( x \) and \( b \) based on the solution?
4. What are the implications if \( b = 0 \)?
5. How would you solve the equation if it were quadratic, such as \( bx^2 - 3b + 6 = 0 \)?

**Tip:** When simplifying fractions, always check if each term can be divided by the common denominator to reduce the expression.

Learn how to solve the linear equation bx - 3b + 6 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating variables and simplifying expressions. Suitable for students in Grades 8-10.

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