In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 6x-y, for x=3 and y=8

Verified step by step guidance

1. Substitute the given values of the variables into the algebraic expression. Replace x with 3 and y with 8 in the expression 6x - y.
2. The expression becomes 6(3) - 8. Simplify the multiplication first by calculating 6 times 3.
3. After performing the multiplication, simplify the expression further by subtracting 8 from the result of 6(3).
4. Verify your work by double-checking the substitution and calculations to ensure accuracy.
5. The simplified result represents the value of the expression for the given values of x and y.

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a value that can change depending on the values assigned to its variables. For example, in the expression 6x - y, 'x' and 'y' are variables that can take on different numerical values.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. This is a fundamental technique in algebra that allows us to evaluate expressions. In the given problem, substituting x with 3 and y with 8 transforms the expression 6x - y into 6(3) - 8.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations are performed in an expression. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules ensures that expressions are evaluated correctly, such as calculating multiplication before subtraction in the expression 6(3) - 8.