Algebraically refers to solving problems or finding solutions using algebraic methods. It involves manipulating equations and expressions using mathematical operations such as addition, subtraction, multiplication, division, factoring, etc.
Imagine you are trying to solve a puzzle with numbers and symbols. You can rearrange the pieces and perform different operations on them until you find the solution. Similarly, in calculus, solving problems algebraically means using mathematical operations to rearrange equations or expressions until you find the desired result.
Analytically: A broader term that encompasses both algebraic and numerical methods for solving problems or finding solutions.
Symbolic Manipulation: The process of manipulating mathematical symbols according to predefined rules without assigning specific values to variables.
Equation Solving Techniques: Various strategies used in mathematics to solve equations systematically, such as isolating variables, applying inverse operations, factoring polynomials, etc.
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