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Introduction to Problem Solving definitions

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  • Linear Equation
    An algebraic statement where variables are raised only to the first power and represent straight-line relationships.
  • Variable
    A symbol used to represent an unknown quantity, often assigned to clarify problem context and relationships.
  • Perimeter
    The total distance around a shape, calculated by summing all side lengths, often modeled with algebraic expressions.
  • Equation
    A mathematical statement showing equality between two expressions, used to model and solve real-world scenarios.
  • Consecutive Integer
    Whole numbers that follow each other in order on the number line, differing by one.
  • Consecutive Even Integer
    Even numbers that follow each other in order, each differing by two from the previous.
  • Consecutive Odd Integer
    Odd numbers that follow each other in order, each differing by two from the previous.
  • Substitution
    Replacing a variable with its equivalent value or expression to simplify and solve equations.
  • Model
    A representation, often visual or algebraic, used to describe and analyze a real-world situation.
  • Context
    The real-world scenario or background in which a mathematical problem is set, guiding interpretation of solutions.
  • Sum
    The result of adding two or more numbers, frequently used to set up equations in word problems.
  • Number Line
    A visual tool displaying numbers in order, useful for understanding relationships like consecutive values.
  • Dimension
    A measurable extent, such as length or width, often used to describe geometric figures in problems.
  • Check
    The process of verifying a solution by plugging values back into equations and assessing reasonableness.
  • Translation
    Converting verbal statements or relationships into algebraic expressions for problem solving.