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Understanding Variables, Coefficients, and Expressions in Algebra

This guide explains fundamental concepts in algebra, focusing on variables, coefficients, constants, and terms. A variable represents a number (e.g., x in 4x), while a coefficient is a numerical factor of a term (e.g., 4 in 4x). A constant is a term without a variable (e.g., 5). An expression is a mathematical phrase that combines these elements (e.g., 4x + 7). We also discuss how to evaluate algebraic expressions by substituting known values for variables and applying the order of operations.

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Understanding Variables, Coefficients, and Expressions in Algebra

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  1. EXPRESSIONS

  2. Vocabulary • A variable is a symbol, usually a letter, used to represent a number. • Example: 4x (x is the variable) • A coefficient is the number factor of a term that contains a variable. • Example: 4x (4 is the coefficient) • A constant is a term without a variable. • Example: 5 • A term of an expression is a number, variable, or the product of both. • Example: 4x + 7 (4x is a term, and 7 is a term)

  3. Vocabulary • An expression is a mathematical phrase that can contain variables, numbers and/or symbols. • Example: 4x + 7 • An algebraic expression is an expression that contains a variable, a number, and at least one operation symbol. • Example: 4 + x • When you substitute a number in for a variable, the algebraic expression becomes the numerical expression. • Example: 4 + x, x = 5 4 + 5

  4. EvaluatingExpressions • To evaluate an algebraic expression, replace the variable or variables with the known values and then use the order of operations. • Example 1: Evaluate the following expression if a=5, b=4, and c=8. 4a – 3b + 1 4(5) – 3(4) + 1 20 – 12 + 1 8 + 1 9

  5. Example 2 • Evaluate the following expressions if m = 9, n = 2, and p = 5. 1. 25 – 5p 2.3. n² + 5n - 6 25 – 5(5) 25 – 25 0 29 (2)² + 5(2) – 6 4 + 10 – 6 14 – 6 8

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