Chapter 1: Linear Equations in One Variable (1.1)

Vocabulary flashcards covering key concepts from Section 1.1: Linear Equations in One Variable, including definitions of equations, solutions, linear form, and properties of equality.

Equation

A statement that two quantities are equal.

Solution

A value of the variable that makes the equation true.

Solution set

The set of all solutions to an equation.

Linear equation in one variable

An equation that can be written in the form ax + b = c with a ≠ 0; it is a first-degree equation because the variable x has an exponent of 1.

First-degree equation

Another name for a linear equation in one variable; the highest power of x is 1.

ax + b = c

The standard form of a linear equation in one variable (a ≠ 0).

Addition property of equality

If a = b, then a + c = b + c.

Subtraction property of equality

If a = b, then a − c = b − c.

Multiplication property of equality

If a = b, then ac = bc.

Division property of equality

If a = b, then a/c = b/c, provided c ≠ 0.

Clearing fractions

A method to remove fractions by multiplying both sides by a common denominator.

Clearing decimals

A method to remove decimals by multiplying both sides by a power of 10.

Conditional equation

An equation that is true for some values of the variable but false for other values.

Contradiction

An equation that has no solution.

Identity

An equation that is true for all real numbers.