0Class 8 Mathematics – Linear Equations in One Variable
1. Introduction
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A linear equation in one variable is an equation in which the variable appears only to the first power.
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It represents a straight line when visualized graphically.
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The equation involves constants and one unknown.
Key Concept:
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Linear equations have exactly one variable and no powers higher than one.
2. General Form
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A linear equation can be written in a general form as a combination of a variable and constants.
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The variable appears only once, and its power is one.
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Examples include expressions like “something with x equals something else.”
3. Solutions of Linear Equations
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A solution is a number that, when substituted in place of the variable, makes the equation true.
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Steps to find the solution:
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Simplify both sides if needed.
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Isolate the variable on one side.
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The number obtained is the solution.
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Check: Substitute the solution back into the original equation to verify it satisfies the equation.
4. Properties of Linear Equations
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Equations can be simplified by performing the same operation on both sides (addition, subtraction, multiplication, division).
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Addition property: You can add or subtract the same quantity from both sides without changing the solution.
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Multiplication property: You can multiply or divide both sides by a non-zero number without changing the solution.
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Unique Solution: Most linear equations in one variable have exactly one solution.
5. Applications
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Linear equations are used in:
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Solving real-life problems involving money, age, distance, and speed.
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Word problems that can be translated into a linear equation.
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Basic algebraic modeling of everyday situations.
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6. Key Points to Remember
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Linear equations have variables with power 1 only.
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Solution is the value of the variable that satisfies the equation.
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Operations performed on both sides must be the same.
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Can be used to solve practical problems.
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Always verify the solution by substituting back into the original equation.
