To solve for \( b \) in the equation:

\[
g = ac + bd
\]

We need to isolate \( b \). Here's the step-by-step solution:

### Step 1: Subtract \( ac \) from both sides
\[
g - ac = bd
\]

### Step 2: Divide both sides by \( d \)
\[
b = \frac{g - ac}{d}
\]

Thus, the solution for \( b \) is:

\[
b = \frac{g - ac}{d}
\]

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

Here are 5 related questions for further exploration:
1. How would the solution change if \( d = 0 \)?
2. Can you solve for \( c \) in the equation \( g = ac + bd \)?
3. What happens if all terms \( g \), \( a \), \( c \), \( b \), and \( d \) are expressed as functions?
4. How would you solve the equation if it included an additional term, \( e \), such as \( g = ac + bd + e \)?
5. How can you check if your solution for \( b \) is correct?

**Tip:** Always check whether variables in the denominator are non-zero to avoid undefined solutions.

Learn how to solve for b in the equation g = ac + bd with this step-by-step guide. Understand key algebraic concepts and the formula b = (g - ac) / d. Suitable for students in Grades 8-10.

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