Linear expressions are algebraic expressions that represent straight lines when graphed, consisting of variables and constants combined using only addition, subtraction, and multiplication by a constant. They form the foundation for understanding linear equations and inequalities, and are crucial in solving real-world problems involving proportional relationships.

Linear Expressions

Linear expressions

Algebraic expressions are mathematical phrases that can contain numbers, variables, and operations, representing a specific value or set of values. They form the foundation of algebra, allowing for the manipulation and simplification of equations to solve for unknowns.

algebraic expressions

straight lines

variables and constants

Addition is a fundamental arithmetic operation that combines two or more numbers to yield a sum, serving as the basis for more complex mathematical concepts. It is commutative and associative, allowing for flexible manipulation and calculation in various mathematical contexts.

addition

Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers, typically by removing the value of one number from another. It is essential for understanding concepts of negative numbers, inverse operations, and is widely used in various real-world applications such as calculating change, measuring differences, and solving equations.

subtraction

multiplication by a constant

Linear equations are algebraic expressions where each term is either a constant or the product of a constant and a single variable, and they graph as straight lines. Solving these equations involves finding the value of the variable that makes the equation true, often using methods like substitution or elimination.

linear equations

Inequalities are mathematical expressions that describe the relative size or order of two values, often represented using symbols like <, >, ≤, and ≥. They are crucial in various fields for solving problems involving limits, optimization, and constraints, offering insights into relationships and conditions within equations and real-world scenarios.

inequalities

real-world problems

A proportional relationship is a relationship between two quantities where their ratio remains constant. This means that as one quantity changes, the other changes in a way that the ratio of the two quantities is always the same.

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