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# Algebra II Unit One

### Dr. Pittman's 1st Semester Course

TermDefinition
Reflexive Property of Equality The property that a = a. One of the equivalence properties of equality
Symmetric Property of Equality Definition: If a = b, then b = a. Example of the Symmetric Property of Equality Equation 1: 5x + 20 = 35 Equation 2: 35 = 5x + 20 In spite of the rearranged terms, Equation 1 and Equation 2 are identical.
Transitive Property of Equality If a = b and b = c, then a = c. One of the equivalence properties of equality. Note: This is a property of equality and inequalities. One must be cautious, however, when attempting to develop arguments using the transitive property in other settings.
Substitution Property of Equality The substitution property of equality that, if a = b, then b can be substituted for a in any equation without changing the truth value of the equation. For example: •Let a = b. •Let d = a + 2. •Then d = b + 2.
Variable A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable
Constant A fixed value. Example: in 2 + 6 = 8, 2, 6, and 8 are constants. Sometimes an a, b, or c can also be a constant.
Numerical Expression A numerical expression is a combination of numbers and one or more operation symbols. Example: 23 + 15 – 8 or 2x -6
Variable Expression A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression c
Evaluate To calculate the value of a word problem or a equation.
Solution Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities.
Properties of Equality Properties and algebra rules for manipulating equations. Operations Addition: If a=b then a+c=b+c.Subtraction: If a=b then a–c=b–c. Multiplication: If a=b then ac=bc. Division: If a=b and c≠0 then a/c=b/c. Reflexive Property a=a Symmetric Property If a=b
Distributive Property
Proof
Identity An equation which is true regardless of what values are substituted for any variables. Identities: 1 + 1 = 2 (x + y)2 = x2 + 2xy + y2 a^2 ≥ 0 sin2 θ + cos2 θ = 1
Multiplication Property of Equality
Division Property of Equality
Extraneous Solution
No Solution
Literal Equation