Linear & Rational Equations Flashcards
Terms for Solving Equations- Algebraic Expression
A mathematical sentence containing algebraic symbols such as numbers, variables, operators*, and grouping symbols.
*an operator must be paired with an operand to be an expression
Terms for Solving Equations- Algebraic Equation
A mathematical sentence that has two algebraic expressions equal to each other.
Terms for Solving Equations- Solution
A value (or values) that make the equation true when substituted into the equation for the variable.
Terms for Solving Equations- Solution Set
The set of all solutions for a given equation.
Terms for Different Types of Equations- Linear Equation (1-Variable)
An equation that can be written in the form ax + b = 0. (Where a and b are real numbers and a does not equal 0).
Terms for Different Types of Equations- Polynomial Equation
An equation that can can be written as a sum (or difference) of terms with the form axn where all coefficients (a) are real numbers and all exponents (n) are whole numbers.
Terms for Different Types of Equations- Rational Equation
An equation that can be written as a ratio of two polynomial equations. (Where the denominator is not equal to zero.)
Terms for Classifying Equations by Solution Set- Conditional Equation
An equation that is true for some values of the variable and false for other values.
Terms for Classifying Equations by Solution Set- Contradiction (Inconsistent) Equation
An equation that is false for all values of the variable.
Terms for Classifying Equations by Solution Set- Identity Equation
An equation that is true for all the values of the variable for which the expressions of the equation are defined.
Equality Property of Addition and Subtraction
if a = b , then a +/- c = b +/- d where a, b, and c are real numbers.
Equality Property of Multiplication and Division
if a = b , then a | / c = b| /d where a, b, and c are real numbers.
Distributive Property of Multiplication over Addition
if a, b, and c are real numbers, then a(b + c) = ab + ac
Solving a Rational Equation
Find the Lowest Common Denominator (LCD)
Identify any Restrictions on the Variable by setting the LCD equal to zero
Convert all Denominators to the LCD
Multiply by the LCD to remove the fractions
Solve the remaining equation by isolating the variable
Check Your Solution(s) against the restrictions. If a possible solution is not a restriction, then the possible solution is a solution to the equation. (If a possible solution is a restriction, then the possible solution is NOT a solution to the equation and is called an extraneous solution.)
