How are algebraic expressions evaluated?

• A. Graphing to approximate values
• B. Substituting numbers and checking only for zero values
• C. Rewriting as a sequence of operations
• D. Substitution and the order of operations

Answer: (D)

Evaluating an algebraic expression means finding its numeric value by replacing each variable with a specific number and then simplifying using the order of operations. You begin by substituting numbers for the variables, then you follow the rules: handle parentheses first, apply any exponents, do multiplication and division from left to right, and finally do addition and subtraction from left to right. For example, if the expression is 3x + 2y and x = 4, y = -1, you substitute to get 3(4) + 2(-1) = 12 - 2 = 10. Following the order of operations ensures you get the correct result, no matter how you compute it.

Graphing to approximate values isn’t how you determine a specific numerical value for an expression. Substituting numbers and checking only for zero values misses the overall value the expression takes when numbers are plugged in. Rewriting as a sequence of operations captures part of the process, but you still need to substitute actual numbers first to obtain the numeric result. The key idea is substitution plus applying the order of operations.