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

\[
5a - 2b = 40
\]

Follow these steps:

1. Isolate \( -2b \) by subtracting \( 5a \) from both sides:

\[
-2b = 40 - 5a
\]

2. Solve for \( b \) by dividing both sides by \( -2 \):

\[
b = \frac{40 - 5a}{-2}
\]

3. Simplify the expression:

\[
b = \frac{-40 + 5a}{2}
\]

4. The final solution is:

\[
b = \frac{5a - 40}{2}
\]

Would you like more details on this solution or have any further questions?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the constant on the right side was different?
2. What happens to the value of \( b \) if \( a \) is negative?
3. How can you verify if your solution for \( b \) is correct?
4. How would you graph the relationship between \( a \) and \( b \)?
5. Can this equation be solved using substitution if more variables are introduced?

**Tip:** Always check your solution by substituting the value of the variable back into the original equation to verify correctness.

Learn how to solve the linear equation 5a - 2b = 40 for b with a step-by-step guide. This problem covers key algebraic concepts and demonstrates how to isolate and solve for a variable. Suitable for students in Grades 7-9.

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