To solve the equation \( A = \frac{1}{2}h(b + c) \) for \( b \), follow these steps:

1. **Multiply both sides by 2 to eliminate the fraction:**

   \[
   2A = h(b + c)
   \]

2. **Divide both sides by \( h \) to isolate \( b + c \):**

   \[
   \frac{2A}{h} = b + c
   \]

3. **Subtract \( c \) from both sides to solve for \( b \):**

   \[
   b = \frac{2A}{h} - c
   \]

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

\[
b = \frac{2A}{h} - c
\]

Would you like any further details or have any questions?

Here are five related questions:
1. How would you solve for \( c \) instead of \( b \) in the same equation?
2. What happens to the equation when \( h = 0 \)?
3. Can you solve for \( h \) in terms of \( A \), \( b \), and \( c \)?
4. How does this equation relate to the area of a trapezoid?
5. What would the equation look like if \( b \) and \( c \) were equal?

**Tip:** When manipulating equations, always perform the same operation on both sides to maintain equality.

Learn how to solve the equation A = 1/2h(b + c) for b with a step-by-step solution. This problem involves manipulating algebraic equations and isolating variables. Suitable for students in Grades 9-12.

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