NCERT Class 7 Maths Chapter 15
Finding the Unknown
This chapter from Ganita Prakash Part 2 introduces CBSE Class 7 students to solving linear equations with one variable. Students learn to set up and solve equations by balancing both sides, using inverse operations, and applying the concept of equality. The chapter connects algebraic thinking to real-life situations such as age problems, money problems, and geometric problems.
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Key Terms
- Linear Equation
- An algebraic equation in which the variable appears with a power of 1 (no squares or higher powers). It represents a straight line when graphed. Example: 2x + 5 = 11.
- Solution of an Equation
- The value of the variable that makes both sides of an equation equal. For example, x = 3 is the solution of 2x + 5 = 11 because 2(3) + 5 = 11.
- Transpose
- Moving a term from one side of an equation to the other, changing its sign in the process. Used to isolate the variable while maintaining balance.
- Balancing Method
- A method of solving equations by performing the same mathematical operation on both sides, keeping the equation balanced like a weighing scale.
- Inverse Operation
- The opposite mathematical operation used to undo an operation. For example, addition and subtraction are inverse operations; multiplication and division are inverse operations.
- Verification
- The process of checking a solution by substituting it back into the original equation to confirm that both sides are equal.
Frequently Asked Questions
What is a linear equation in one variable?▾
A linear equation in one variable is an equation with exactly one unknown, where the variable has a power of 1. It is of the form ax + b = c, where a, b, and c are numbers and x is the unknown. For example, 3x – 4 = 11 is a linear equation.
How do you solve a linear equation?▾
To solve a linear equation, isolate the variable on one side by performing inverse operations on both sides. For example, to solve 3x – 4 = 11: add 4 to both sides to get 3x = 15, then divide both sides by 3 to get x = 5.
What is the transposition method for solving equations?▾
In the transposition method, terms are moved from one side of the equation to the other by changing their sign. For example, in 2x + 7 = 15, transpose 7 to the right side: 2x = 15 – 7 = 8, then x = 4.
How do you verify the solution of an equation?▾
Substitute the found value back into the original equation and check if both sides are equal (LHS = RHS). For example, if x = 4 is the solution of 2x + 7 = 15: LHS = 2(4) + 7 = 8 + 7 = 15 = RHS. The solution is verified.
How do you form an equation from a word problem?▾
Identify the unknown and assign it a variable. Translate the conditions of the problem into an algebraic equation. For example, 'A number increased by 12 gives 35' becomes n + 12 = 35. Solve to get n = 23.
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