Linear expressions are fundamental algebraic statements with variables and constants, where variables are to the first power. Understanding their components—variables, terms, and coefficients—is crucial for simplifying and solving linear equations and inequalities. This knowledge also aids in translating word problems into algebraic expressions and graphing linear equations to visualize their solutions.
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Linear expressions are algebraic statements composed of variables and constants, with each variable raised to the first power
Variables
Variables are symbols that represent unknown values in a linear expression
Terms
Terms are the distinct elements of an expression that are combined using addition or subtraction
Coefficients
Coefficients are the numerical factors that multiply the variables within terms in a linear expression
Word problems can be translated into linear expressions by identifying key words that correspond to mathematical operations
Simplifying linear expressions involves rewriting them in their most reduced form while maintaining their original value
Distributing Multiplication
Distributing multiplication over addition or subtraction is a common method for simplifying linear expressions
Combining Like Terms
Combining like terms is another method for simplifying linear expressions
Simplifying Constants
Simplifying constants, such as adding or subtracting them, is also important in simplifying linear expressions
Linear equations are algebraic statements that equate two linear expressions
Types of Linear Equations
Linear equations with one variable result in vertical or horizontal lines, while those with two variables result in straight lines
Determining Slope and Y-Intercept
The slope and y-intercept of a linear equation can be determined from its standard form or slope-intercept form
Single-Variable Equations
Solving single-variable linear equations involves isolating the variable on one side of the equation
Two-Variable Systems
Two-variable linear equations can be solved using methods such as substitution or elimination
Linear Inequalities
Linear inequalities use symbols like '<', '>', '≤', and '≥' and are solved to find a range of values that satisfy the inequality
00
The expression '3x + 5' is considered ______ because 'x' is not raised to any power higher than ______.
linear
one
01
Define variables in linear expressions.
Variables are symbols representing unknown values, typically denoted by letters.
02
Identify terms in a linear expression.
Terms are elements of an expression combined using addition or subtraction, like '5x' or '-2'.
