Which statement represents the proper way to simplify the expression: 5b + 3b - 2b?

• A. You cannot combine terms with different variables
• B. Add to obtain 6b
• C. Add to obtain 7b - 2b
• D. Subtract to simplify to 3b

Answer: (B)

The correct interpretation of how to simplify the expression 5b + 3b - 2b involves combining like terms, which are all terms that share the same variable (in this case, "b"). When simplifying, you first group the coefficients of these terms together.

Starting with the expression, you combine the coefficients: 5 (from 5b) and 3 (from 3b), which adds up to 8. Then, you subtract 2 (from -2b) from this sum.

So, the calculation proceeds as follows:

5b + 3b results in 8b, and then subtracting 2b gives us:

8b - 2b = 6b.

Thus, the final simplified form of the expression is 6b. This step-by-step combination of coefficients is fundamental in algebra for simplifying expressions correctly, and it demonstrates the ability to handle like terms appropriately in algebraic expressions.