Ths video lesson is about algebraic equations in one variable
Introduction to CBSE Class 8 Mathematics Chapter "Linear Equations in One Variable"
The “Linear Equations in One Variable” chapter from CBSE Class 8 Mathematics forms the foundation of algebra for students. This chapter teaches students about linear equations, which are algebraic expressions that represent a line in a singular variable. The students explore equations that involve constants, coefficients, and variables leading to a better understanding of how to manipulate and solve for the unknown.
It breaks down the concepts of solving linear equations by transposing terms, using inverse operations, and simplifying expressions. The chapter also addresses practical applications of linear equations in solving problems related to geometry, ratios, percentages, and other real-life situations. Concepts like “solution of an equation” and “solving equations having the variable on both sides” are explained with step-by-step examples.
Assignments for CBSE Class 8 Mathematics Chapter “Linear Equations in One Variable”
- Solve the Real-World Problems: Create word problems involving age, distance, or money that can be solved using linear equations.
- Equation Solving Marathon: Solve a set of 20 linear equations with increasing complexity and document the solving process.
- Balancing Equations: Illustrate the balance method with graphical aids to solve linear equations.
- Daily Applications: Identify and describe situations in daily life where linear equations could be applied and solve them.
- Creative Equations: Write a short story that includes a problem that can be solved by a linear equation, then solve it within the narrative.
Conclusion The chapter “Linear Equations in One Variable” is crucial as it provides the tools for problem-solving not only in mathematics but also in real-life scenarios. It is an excellent foray into the universe of algebra and prepares students for more advanced concepts, enhancing their logical thinking and analytical skills.
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Questions and Answers for CBSE Class 8 Mathematics Chapter "Linear Equations in One Variable"
- Q1: What is a linear equation in one variable?
ANS: A linear equation in one variable is an equation that can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable. - Q2: How do you solve a linear equation?
ANS: To solve a linear equation, isolate the variable on one side of the equation using inverse operations and simplification. - Q3: Can a linear equation have more than one solution?
ANS: Generally, a linear equation in one variable has a single unique solution. However, some equations may have infinitely many solutions or no solution at all. - Q4: What does it mean to ‘transpose’ in solving equations?
ANS: Transposing means moving a term from one side of the equation to the other by changing its sign to maintain equality. - Q5: Why are linear equations important?
ANS: Linear equations are important because they help in finding unknown values and are widely used in various fields such as science, engineering, and economics. - Q6: What are the applications of linear equations in real life?
ANS: Linear equations are used in budgeting, calculating distances, determining trends, and in various situations that require decision-making. - Q7: How can we check the solution of a linear equation?
ANS: The solution can be checked by substituting the value of the variable back into the original equation and verifying that both sides are equal. - Q8: What is an ‘inverse operation,’ and how is it used?
ANS: An inverse operation is used to cancel out an operation on one side of an equation to help isolate the variable, such as using addition to cancel subtraction. - Q9: How do you solve equations with variables on both sides?
ANS: To solve equations with variables on both sides, first simplify both sides, if necessary, then use inverse operations to get all terms with variables on one side and the constant terms on the other. - Q10: Can linear equations be graphed?
ANS: Yes, linear equations in one variable can be graphed on a number line, showing the point where the value of the variable satisfies the equation.
