Chapter 1-7: Linear Equations Vocabulary

Vocabulary flashcards covering key terms from the lecture notes on linear equations, fractions, and related algebraic concepts.

Linear equation

An equation of the form Ax + B = 0 with A ≠ 0; represents a straight line and has degree 1.

Equation

A statement that two expressions are equal, connected by an equals sign.

LCD (Least Common Denominator)

The smallest expression that is divisible by all denominators in the equation (the least common multiple of the denominators).

Clear the fractions

The process of eliminating fractions by multiplying every term by the LCD to obtain an equivalent equation without fractions.

Distributive property

The rule a(b + c) = ab + ac; used to distribute multiplication over addition when expanding.

Multiplication property of equality

If a = b, then ac = bc for any c; used to multiply both sides of an equation by the same quantity.

Addition/Subtraction property of equality

If a = b, then a ± c = b ± c; allows moving terms between sides by adding or subtracting the same value.

Foil

First, Outer, Inner, Last; a method to multiply two binomials by distributing each term in the first binomial with each term in the second.

Quadratic equation

An equation containing a squared term (x^2); often written as ax^2 + bx + c = 0 and may reduce to a linear equation if x^2 terms cancel.

Leading term

The term with the highest power of the variable in a polynomial; used to determine degree and cancellations.

Like terms / Similar terms

Terms that have the same variable raised to the same power; can be combined (e.g., 3x and 5x).

Rational equation

An equation in which the expressions are fractions (rational expressions); solved by clearing denominators using the LCD.

Rational expressions

Expressions that are ratios of polynomials or algebraic expressions.

Undefined

A value or expression is undefined if a denominator becomes zero, making the expression invalid.

Solution

The value(s) of the variable that satisfy the equation; often written in braces, e.g., { -7 } or { -7, 5 }.