Simple Equations
Overview
Simple Equations is a fundamental chapter in Class 7 Mathematics that introduces students to the concept of an equation, its components, and methods to solve it. An equation is a statement of equality containing one unknown variable. Students learn to set up equations from real-life situations and solve them using systematic methods like transposition and the balance method, building a strong foundation for algebra in higher classes.
Typed Notes
What is an Equation?
An equation is a mathematical statement that says two expressions are equal. For example, 2x + 3 = 11 is an equation where x is the unknown variable. The expression on the left of '=' is the Left Hand Side (LHS) and on the right is the Right Hand Side (RHS). An equation is like a balance scale — both sides must always remain equal. A value of the variable that satisfies the equation (makes LHS = RHS) is called the solution or root of the equation.
Solving Equations — Balance Method
In the balance method, we perform the same mathematical operation on both sides of the equation to keep it balanced. To solve 2x + 3 = 11, subtract 3 from both sides: 2x = 8. Then divide both sides by 2: x = 4. We can verify by substituting x = 4 back: LHS = 2(4) + 3 = 11 = RHS. This method works for all linear equations in one variable and helps students understand why the steps are logically valid and not just mechanical tricks.
Transposition Method
Transposition is a shortcut of the balance method. When a term is moved from one side of the equation to the other, its sign changes: addition becomes subtraction, multiplication becomes division, and vice versa. For example, in 3x − 5 = 10, transpose −5 to the RHS: 3x = 10 + 5 = 15, then transpose 3 (which multiplies x) to RHS: x = 15 ÷ 3 = 5. Always transpose numbers first, then the coefficient of the variable. Verify the answer by substituting back into the original equation.
Setting Up Equations from Word Problems
Many real-life situations can be expressed as simple equations. The key step is to identify the unknown and represent it with a variable. For example, 'Raju's age is 5 more than twice his sister's age. If Raju is 17, find his sister's age.' Let sister's age = x. Then 2x + 5 = 17. Solving: 2x = 12, x = 6. His sister is 6 years old. Carefully reading the problem, choosing the right variable, and translating words into mathematical expressions are the essential skills for this type of question.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01An equation has two sides — Left Hand Side (LHS) and Right Hand Side (RHS) — connected by an equal sign.
- 02A solution (or root) of an equation is the value of the variable that makes LHS equal to RHS.
- 03Adding, subtracting, multiplying, or dividing both sides by the same number keeps the equation balanced.
- 04Transposition means moving a term from one side to the other by changing its sign (+ becomes −, × becomes ÷).
- 05Any real-life problem can be converted into an equation by representing the unknown quantity with a variable like x, y, or n.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Solve: 4x + 7 = 23
Solve: 3y − 9 = 0
The sum of three consecutive integers is 48. Find the integers.
Solve: (x/5) + 3 = 7
Meena is 6 years older than her brother. If the sum of their ages is 28, find their ages.
Simple Equations deals with finding the unknown value of a variable using the balance method or transposition. An equation remains valid as long as the same operation is applied to both sides. Transposition moves terms across the equal sign with a change in sign. Word problems are solved by expressing the unknown as a variable, forming an equation, and solving it systematically. Always verify the solution by substituting back into the original equation.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which value of x satisfies the equation 5x − 10 = 15?
Q2.What is the process of moving a term from one side of an equation to the other called?
Q3.If 2n + 4 = 14, what is the value of n?
Q4.Which of the following is NOT an equation?
Mark karo — dashboard par progress dikhega.