Section 2.1: Linear Equations in One Variable

Vocabulary flashcards covering fundamental definitions, properties, and types of solutions for linear equations in one variable from Section 2.1.

Linear Equation in One Variable

An equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$.

Equation

A mathematical statement that contains an equal sign ($=$) and can be solved.

Expression

A mathematical combination of terms that does not contain an equal sign ($=$) and cannot be solved.

Addition Property of Equality

The property stating that adding or subtracting the same number to each side of an equation does not change the solution set; if $a = b$, then $a + c = b + c$.

Multiplication Property of Equality

The property stating that multiplying or dividing each side of an equation by the same nonzero number does not change the solution set; if $a = b$ and $c \neq 0$, then $ac = bc$.

Least Common Denominator (LCD)

The smallest denominator that all denominators in an equation can divide into, used to eliminate fractions by multiplying each term by it.

One Solution

A type of linear equation solution where solving yields a single numeric answer ($x = \text{some number}$), with a solution set of $\{\text{the number you solved to get}\}$.

All Real Numbers Solution

A type of linear equation solution where solving causes variables to cancel and leaves a true statement, with a solution set of $\{\text{All Real Numbers}\}$.

No Solution

A type of linear equation solution where solving causes variables to cancel and leaves a false statement.