To solve for \( b \) in the equation \( z = \frac{a + b}{c} \), follow these steps:

### Step 1: Eliminate the denominator
Multiply both sides of the equation by \( c \) to get rid of the fraction:

\[
z \cdot c = a + b
\]

### Step 2: Isolate \( b \)
Now, subtract \( a \) from both sides to solve for \( b \):

\[
b = z \cdot c - a
\]

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

\[
b = zc - a
\]

Would you like a further breakdown or have any questions?

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Here are five related questions to deepen your understanding:

1. If \( z = 5 \), \( a = 2 \), and \( c = 3 \), what is the value of \( b \)?
2. How would the solution change if \( c = 0 \)?
3. Can this formula \( b = zc - a \) be used for complex numbers \( a, b, c, z \)?
4. What happens to \( b \) if \( z \) and \( c \) are both negative?
5. What is the geometric interpretation of this formula?

**Tip:** Always check whether division by zero is involved when solving equations with fractions.

Learn how to solve for b in the equation z = (a + b) / c with a clear step-by-step explanation. This problem introduces basic algebraic concepts like solving for a variable and manipulating linear equations. Ideal for students in Grades 6-8.

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