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Numbers, Algebra, Discrete vs Continuous
Equation
An equation states that two expressions are equal.
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Equation
Definition
An equation states that two expressions are equal.
Example:
x + 1 = 4
Left side:
x + 1
Right side:
4
Equation = equality claim between two expressions.
Equation vs Expression
Expression:
x + 1
Equation:
x + 1 = 4
The expression describes a quantity.
The equation claims two quantities are equal.
An equation contains a relationship of equality.
Solution
A solution is a value that makes the equation true.
Example:
x + 1 = 4
If:
x = 3
then:
3 + 1 = 4
So x = 3 is a solution.
Solving means finding values that make equality true.
True Or False
Some equations have no unknowns.
Example:
2 + 2 = 4
This is true.
Example:
2 + 2 = 5
This is false.
An equation can be a statement, not only a problem to solve.
Multiple Or No Solutions
Some equations have one solution.
x + 1 = 4
Some have many solutions.
x = x
Some have no solution.
x + 1 = x
The structure of the equation determines its solution behavior.
Final Summary
- An equation states equality between two expressions.
- Expressions are parts of equations.
- A solution makes the equation true.
- Equations can be true, false, or contain unknowns.
- Equations can have one solution, many solutions, or no solution.
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Continue the series.
Closed-Form Solution