N-Gen Math Algebra I: Unit 2 Review - Linear Equations and Inequalities

Vocabulary and conceptual terms covering linear equations, inequalities, algebraic modeling, literal equations, and properties of equality from N-Gen Math Algebra I Unit 2 Review.

Equation

A mathematical statement asserting the equality ($=$) of two expressions, distinct from an algebraic expression (such as $4x - 1$) which makes no statement of equality.

Solution to an Equation

A value of a variable that makes an equation a true statement when substituted; for instance, $x = 4$ is a solution to $2x + 7 = 15$ because substituting $4$ produces a true equality ($15 = 15$).

Addition Property of Equality

The algebraic property stating that adding the same number or expression to both sides of an equation maintains equality, such as adding $-7$ to both sides of $4x + 7 = 10$.

At Least

A verbal phrase translating to the inequality symbol for "greater than or equal to" ($\ge$), denoting that a quantity must be equal to or larger than a given boundary.

At Most

A verbal phrase translating to the inequality symbol for "less than or equal to" ($\le$), denoting that a quantity cannot exceed a given boundary.

Consecutive Odd Integers

Odd integers that follow each other in order without gaps, algebraically represented as $n$ and $n + 2$, whose sum is modeled as $n + (n + 2)$.

Inequality Sign Reversal Rule

The operational rule dictating that multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol (e.g., transforming $<$ to $>$ or $\le$ to $\ge$).

Literal Equation

An equation consisting primarily of multiple variables (letters) that can be solved algebraically to express one targeted variable in terms of all other variables involved (e.g., isolating $x$ in $\frac{2x}{a} + b = c$).

Perimeter Model for a Rectangle

An equation representing the total distance around a rectangle using its dimensions, formulated as $2(\text{length} + \text{width}) = \text{perimeter}$ (e.g., $2(2w + 6 + w) = 120$).

Algebraic Translation of "Three Years Less Than Twice Jody's Age"

The expression $2j - 3$, where $j$ represents Jody's age.

Solution Set of a Linear Inequality

The collection of all real numbers that satisfy an inequality statement; for example, the solution set for $2x + 1 > 15$ is $x > 7$, meaning any choice strictly greater than $7$ makes the statement true.

Multi-Step Linear Equation

An equation that requires multiple algebraic operations—such as applying the distributive property, combining like terms, and clearing decimals or fractions—to isolate the unknown variable.