Chapter 6 - Simple Equations Revision Notes - Class 7 Mathematics

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📌 Key Points

An equation is a statement with two equal expressions separated by '='. Has left side and right side.
A variable (x, y, z) represents an unknown value. Goal is to find its value.
Solution of equation is the value of variable that makes the equation true.
Transposition: Moving a term from one side to other changes its sign (+ to −, − to +, × to ÷, ÷ to ×)
Balance method: Do same operation on both sides. Whatever you do to left, do to right.
To remove +a from side, subtract a from both sides.
To remove −a from side, add a to both sides.
To remove ×a (multiply), divide both sides by a.
To remove ÷a (divide), multiply both sides by a.
Word problems: Identify unknown, assign variable, write equation, solve, check answer.
Always verify solution by substituting back into original equation.
Consecutive integers: If first = x, then next = x+1, x+2, etc.
When equation has brackets like 2(x+3), expand first: 2x + 6.
Linear equation has variable with power 1. Example: 3x + 5 = 14
Order of operations in solving: Simplify brackets first, then isolate variable.

📘 Important Definitions

Equation

A mathematical statement with equal sign showing two expressions are equal. Example: 3x + 5 = 14

Variable

A letter (x, y, z) representing an unknown number whose value we need to find.

Solution

The value of the variable that makes the equation true.

Transposition

Moving a term from one side of equation to another. Sign changes: + becomes −, − becomes +.

Linear Equation

Equation where highest power of variable is 1. Form: ax + b = c

Balance Method

Solving by doing same operation on both sides to keep equation balanced.

Verification

Checking if solution is correct by substituting value back into original equation.

Consecutive Integers

Integers in order: x, x+1, x+2, ... or x-1, x, x+1, ...

🔢 Formulas & Laws

Basic Equation Form

ax + b = c, where a, b, c are constants and x is variable

Solve for x: x = (c - b) / a

Transposition Rule

a - b = a + (-b) (change sign when moving across =)

Moving +a gives −a, moving −a gives +a

Two Consecutive Integers

First = x, Second = x + 1. Sum = 2x + 1

Example: x + (x+1) = 25 gives 2x + 1 = 25

Distributive Property

a(b + c) = ab + ac. Apply before solving.

Example: 2(x + 3) = 2x + 6

Verification Formula

Substitute solution value in original equation. Both sides should be equal.

If x = 4 in 2x + 3 = 11, check: 2(4) + 3 = 11 ✓

⚠️ Common Mistakes

✗ Wrong: Forgetting to change sign during transposition: 3x + 5 = 14 becomes 3x = 14 - 5 ✗ (leaving +5)

✓ Correct: Correct: When moving +5 across =, it becomes −5. So 3x = 14 − 5 = 9

✗ Wrong: Not applying operation to both sides in balance method: x − 3 = 7, add 3 to left only

✓ Correct: Correct: Add 3 to BOTH sides: x − 3 + 3 = 7 + 3, so x = 10

✗ Wrong: Skipping verification: Just state the answer without checking if it's correct

✓ Correct: Correct: Always substitute back. 2x + 5 = 13, if x = 4: 2(4) + 5 = 13 ✓

✗ Wrong: Not expanding brackets first: 2(x + 3) = 10 solved as 2x + 3 = 10

✓ Correct: Correct: Expand first: 2x + 6 = 10, then 2x = 4, x = 2

✗ Wrong: Wrong word conversion: 'A number minus 5 is 12' written as 5 − x = 12

✓ Correct: Correct: x − 5 = 12 (not 5 − x). The unknown comes first usually.

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Solving simple linear equations (transposition or balance method)

2m★★★

Verification of solutions by substitution

1m★★★

Word problems on equations (age, distance, cost problems)

3m★★

Equations with brackets: 2(x + 3) = 14 type

2m★★

Finding consecutive integers with equation

Translating English statements to equations

1m★★

🎯 Last-Minute Recall