Question

Compare and contrast simplifying the numeric expression 3 – (2 + 5) to the algebraic expression 3x – (2x + 5)

Answer 1

With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.

Answer 2

The operations carried out on the numeric expression, such as distribution of the negative sign, addition and subtraction are the same as that for the algebraic expression. However, the presence of the variable x in the algebraic expression means we cannot combine all of the terms, only the like ones.
The numeric one simplifies to:
3 - (2 + 5) = 3 - 7 = -4
While the algebraic one simplifies to:
3x - (2x + 5) = 3x - 2x - 5 = x - 5