Summary
Chapter 2 of Class 8 Maths, 'Linear Equations in One Variable', teaches students how to solve algebraic equations that contain only one variable with a highest power of 1. Students learn to balance equations using transposition and various algebraic methods to find solutions.
This chapter introduces linear equations in one variable, where the highest power of the variable is 1. Students learn the concepts of Left Hand Side (LHS) and Right Hand Side (RHS), how to verify solutions, and multiple methods for solving equations—including equations with variables on both sides. The chapter covers simplifying equations by multiplying by the LCM of denominators, opening brackets, and combining like terms. Real-world applications include solving problems on numbers, ages, perimeters, and currency combinations using linear equations.
Key points & formulas
- 01A linear equation in one variable has only one variable with highest power equal to 1 (e.g., 2x, 3y – 7)
- 02The solution of an equation is the value of the variable for which LHS equals RHS (e.g., x = 5 is a solution of 2x – 3 = 7)
- 03Equations can have variables on both sides; solve by moving variable terms to one side using transposition
- 04To clear fractions, multiply both sides of the equation by the LCM (Least Common Multiple) of all denominators
- 05Simplify equations by opening brackets and combining like terms before applying transposition methods
- 06Verify solutions by substituting back into the original equation to check LHS = RHS
- 07Linear equations solve real-world problems involving numbers, ages, perimeters, and currency combinations
Frequently asked questions
01What is a linear equation in one variable?
A linear equation in one variable is an algebraic equation containing only one variable with highest power equal to 1, such as 2x + 3 = 7 or 5x – 2 = x + 4. It expresses the equality of two expressions using the equals sign.
02How do you solve an equation with variables on both sides?
To solve equations with variables on both sides (like 2x – 3 = x + 2), transpose all variable terms to one side by subtracting or adding, keeping the equation balanced by performing the same operation on both sides. For example, subtract x from both sides to get x – 3 = 2, then solve for x.
03Why do you multiply both sides by the LCM when solving equations with fractions?
Multiplying both sides by the LCM (Least Common Multiple) of the denominators clears fractions, converting the equation into a simpler linear form that is easier to solve. For example, to solve (6x + 1)/3 + 1 = (x – 3)/6, multiply both sides by 6 to eliminate all denominators.
04What does it mean to verify a solution of an equation?
Verifying a solution means substituting the found value back into the original equation to check whether the Left Hand Side (LHS) equals the Right Hand Side (RHS). If LHS = RHS, the solution is correct; if not, there is an error.
05Is the Class 8 Maths Chapter 2 Linear Equations in One Variable PDF free to download?
Yes, the Class 8 Maths Chapter 2 PDF is available free to download with no sign-up required on cbseprepmaster.com. The chapter is part of the NCERT textbook and can be accessed anytime for study and practice.
More chapters in Mathematics
This is the complete Mathematics Chapter 2 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 8 textbooks.
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