Exploring the fundamentals of algebra, this guide delves into equations and inequalities, illustrating their application in real-world scenarios. Equations are mathematical statements of equivalence, while inequalities express ranges of possible solutions. Both concepts are pivotal in modeling situations from budgeting to motion, and understanding them is key to analyzing mathematical relationships and solving complex problems.
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Equations are mathematical statements that show the equivalence of two expressions using an equals sign
Budgeting
Equations can be used to model real-world situations, such as budgeting, to find the value of unknown quantities
Minimum Wage
Equations can also be used to represent minimum wage requirements, where the variable represents the hourly wage
Polynomial equations involve expressions with variables raised to whole number powers and are used to model complex situations
Inequalities are mathematical statements that show a relationship of comparison between two quantities using symbols like >, <, ≥, and ≤
Stipulating Conditions
Inequalities are useful for setting conditions, such as a minimum number of points needed to win a game
Attendance Requirements
Inequalities can also be used to represent attendance requirements, where the variable represents the number of absences allowed
Quadratic inequalities involve terms with variables raised to the second power and are crucial for modeling parabolic relationships
Linear equations and inequalities with two variables involve expressions with two variables and are used to explore relationships between quantities
Solving Systems of Equations
Linear equations and inequalities with two variables can be used to solve systems of equations, such as finding the prices of two items given their total cost and the cost of a different combination of items
Graphical Representations
Linear equations and inequalities with two variables can also be represented graphically on a coordinate plane to show a range of solutions
Quadratic equations and inequalities involve terms with variables raised to the second power and are used to model parabolic relationships
Projectile Motion
Quadratic equations and inequalities are crucial for modeling the path of a projectile, such as a thrown object
Optimization and Motion
Quadratic equations and inequalities are also used to address problems involving area, optimization, and motion
00
In algebra, ______ and ______ are key concepts that express how quantities relate to each other.
Equations
inequalities
01
The equation $40 + x = $100 is used to determine the cost of ______ when the shirt is priced at $40 and the total spending is $100.
shoes
02
Inequality Symbols Meaning
> means greater than, < means less than, ≥ means greater or equal to, ≤ means less or equal to.
