Term | Definition |
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 |
Addition Property of Equality | |
Multiplication Property of Equality | |
Division Property of Equality | |
Extraneous Solution | |
No Solution | |
Literal Equation | |
Commutative Property of Addition | |
Commutative Property of Multiplication | |
Inverse Operations | Operations that undo each other: Ex. 1+5=6 or 5+1=6, additive 6-5=1 or 6-1=5, subtractive a/a= 1, multiplicative |
Absolute Value Equation | |
Inequality Equations | |