Linear Equations for Class 6 ICSE — Maths Chapter 15
Linear equations for class 6 ICSE are the subject of Chapter 15, Simple Linear Equations, in the Class 6 Mathematics book. The chapter defines what an equation is, explains when it counts as linear, and gives four rules for solving it. You will practise each equation form step by step, then apply the same method to word problems that turn sentences into equations.
Download Simple Linear Equations Class 6 ICSE Mathematics Chapter 15 PDF
Download the Simple Linear Equations Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 8 pages, 8 sections, 56 questions.
What is inside Chapter 15
8 pages · 8 sections · 10 worked examples · 56 exercise questions
| Section | Title |
|---|---|
| 15.1 | BASIC CONCEPT |
| 15.2 | SOLVING A LINEAR EQUATION |
| 15.3 | RULES FOR SOLVING A LINEAR EQUATION |
| 15.4 | SOLVING AN EQUATION OF THE FORM x + a = b |
| 15.5 | SOLVING AN EQUATION OF THE FORM x – a = b |
| 15.6 | SOLVING AN EQUATION OF THE FORM ax = b |
| 15.7 | SOLVING AN EQUATION OF THE FORM x/a = b |
| 15.10 | SOLVING WORD PROBLEMS |
- EXERCISE 15(A): 5 questions
- EXERCISE 15(B): 3 questions
- EXERCISE 15(C): 27 questions
- EXERCISE 15(D): 10 questions
- Revision Exercise (Chapter 15): 11 questions
15.1 BASIC CONCEPT
An equation is a mathematical statement that two expressions are equal. The chapter starts with expressions such as 3x - 5 and x + 8. When these are equal, you write 3x - 5 = x + 8. That written statement is an equation.
Word statements turn into equations directly. “Seven subtracted from a number equals 4” becomes x - 7 = 4. “A certain number multiplied by 4 equals 20” becomes 4x = 20. “A number divided by 7 equals 2” becomes \frac{x}{7} = 2.
An equation is linear when it contains only one variable with highest power 1. Every equation above uses only x, raised to the first power. That is why each one is a linear equation.
Try your own: a number multiplied by 5 equals 25. Write it as 5x = 25. One variable, power 1, so it is linear. This is the same idea that runs through the whole Class 6 Maths book.
15.2 SOLVING A LINEAR EQUATION
Solving a linear equation means finding the value of the unknown algebraic quantity in it. For x + 5 = 7, solving means finding x. For 3y + 2 = 9, it means finding y. For \frac{2a}{3} + 4a = 10, it means finding a. The letter does not matter; the process is the same.
The unknown is a placeholder that any letter can fill. Once you find the value, substitute it back into the original equation. Both sides should come out equal. If they do not, check each step again.
Take x + 5 = 7. The aim is a statement of the form x = \text{a number}. Substituting x = 2 gives 2 + 5 = 7, which is true. The solution checks. This check is worth doing on every exercise in this chapter.
15.3 RULES FOR SOLVING A LINEAR EQUATION
The chapter gives four rules that keep an equation true while you work toward the solution. Each rule is one operation applied to the whole equation.
| Rule | What you do | Example |
|---|---|---|
| Rule 1 | Add the same quantity to both sides | x + 5 = 2 \Rightarrow x + 5 + 7 = 2 + 7 |
| Rule 2 | Subtract the same quantity from both sides | x + 5 = 2 \Rightarrow x + 5 - 7 = 2 - 7 |
| Rule 3 | Multiply each term by the same quantity | 5x = 2 \Rightarrow 5x \times 3 = 2 \times 3 |
| Rule 4 | Divide each term by the same non-zero quantity | 3x = 5 \Rightarrow \frac{3x}{3} = \frac{5}{3} |
Why these rules work: if two quantities are equal, doing the same thing to both keeps them equal. Add 7 to both sides of a true equation and it stays true. That balance idea sits behind every step.
Notice the wording. Rules 1 and 2 say “both sides.” Rules 3 and 4 say “each term.” When you multiply or divide, every term in the equation must be treated the same way. Rule 4 also says “non-zero,” because dividing by zero is not allowed.
A common mistake is changing only one side. If you subtract 4 from the left side of 3x - 2 = 8 but not the right, the equation is no longer balanced. Whatever you do to one side, do the same to the other.
15.4 SOLVING AN EQUATION OF THE FORM x + a = b
This form has a number added to the variable, such as x + 3 = 10. To undo the addition, subtract a from both sides. That is Rule 2.
Why: the equation shows x plus a. Subtraction is the inverse of addition. Removing a from both sides leaves x alone on the left.
Solve y + 6 = 15. Subtract 6 from both sides: y + 6 - 6 = 15 - 6. This gives y = 9. The answer is 9.
The exercises include decimals and mixed numbers, such as p + 4.6 = 8.5 and x + 2\frac{1}{3} = 5. The same subtraction rule handles them. Nothing changes except the numbers.
15.5 SOLVING AN EQUATION OF THE FORM x – a = b
This form has a number subtracted from the variable, such as x - 5 = 2. To undo the subtraction, add a to both sides. That is Rule 1.
Why: the equation shows x minus a. Addition is the inverse of subtraction. Adding a to both sides leaves x alone on the left.
Solve x - 4 = 11. Add 4 to both sides: x - 4 + 4 = 11 + 4. This gives x = 15. The answer is 15.
Compare this with section 15.4. There, the equation showed addition, so you subtracted. Here, the equation shows subtraction, so you add. The operation is always the inverse of the one shown.
15.6 SOLVING AN EQUATION OF THE FORM ax = b
This form has the variable multiplied by a number, such as 2x = 6. To undo the multiplication, divide both sides by a. That is Rule 4.
Why: the equation says x times a. Division is the inverse of multiplication. Dividing each term by a leaves x alone.
Solve 5x = 35. Divide each term by 5: \frac{5x}{5} = \frac{35}{5}. This gives x = 7. The answer is 7.
The answer is not always a whole number. For 5x = 2, dividing gives x = \frac{2}{5}. A fraction answer is correct; do not force it into a whole number.
15.7 SOLVING AN EQUATION OF THE FORM x/a = b
This form has the variable divided by a number, such as \frac{b}{2} = 5. It also covers two-step equations and the shortcut called transposition. Three tools appear here: the multiplication rule, two-step solving, and transposition.
The multiplication rule
To undo a division, multiply both sides by the denominator. That is Rule 3. Solve \frac{b}{4} = 3. Multiply each term by 4: \frac{b}{4} \times 4 = 3 \times 4. This gives b = 12. Division is undone by multiplication, the same way addition is undone by subtraction.
Two-step equations
Some equations need two operations. Example: 2x + 5 = 19. First subtract 5 from both sides: 2x = 14. Then divide by 2: x = 7. State which rule you use at each step. First Rule 2 removes the constant, then Rule 4 isolates the variable. The order matters: remove the added term before undoing the multiplication.
Transposition
Transposition is a shortcut. Instead of writing “subtract 9 from both sides,” you move the term to the other side and flip its sign. In transposition, a positive term becomes negative and a negative term becomes positive. Solve x + 9 = 25. Move +9 across: x = 25 - 9. This gives x = 16. Similarly, y - 4 = 3 becomes y = 3 + 4, so y = 7.
Decimals and mixed numbers appear throughout the exercises in this ICSE chapter. The rules handle them exactly as they handle whole numbers. This section closes with three exercise blocks. EXERCISE 15(A) has 5 questions on the basic forms. EXERCISE 15(B) has 3 questions on two-step equations. EXERCISE 15(C) has 27 questions mixing all forms, including negative answers and decimals.
15.10 SOLVING WORD PROBLEMS
Word problems wrap up the chapter. They turn an English sentence into an equation, then you solve it with the same four rules. The chapter gives a four-step method, and the same method appears in later chapters of the Class 6 ICSE books collection.
The four-step method
- Step 1: Read the statement carefully to see what is given and what is asked.
- Step 2: Let the unknown be x, y or z.
- Step 3: Form the equation from the stated relationship between knowns and unknowns.
- Step 4: Solve the equation to get the unknown quantity.
Problem patterns
Most problems fall into a few patterns. A number increased or decreased by a fixed amount. A fraction of a number, such as one-third or one-fifth. Ages of two people with a known difference and sum. Consecutive natural numbers taken as x and x + 1, or x, x + 1, x + 2 for three numbers.
Work through a fresh example: “A number increased by 9 equals 25. Find the number.” Step 1: we must find the number. Step 2: let it be x. Step 3: the relationship is x + 9 = 25. Step 4: solve, x = 25 - 9 = 16. The required number is 16.
Two exercise blocks follow. EXERCISE 15(D) has 10 word problems. The Revision Exercise (Chapter 15) has 11 questions covering all forms and word problems together. For the current syllabus, check the official CISCE website.
What to practise from Linear Equations for Class 6 ICSE
Work through the blocks in order. Each one practises a specific skill from the chapter.
- EXERCISE 15(A) — 5 questions on the four basic forms: x + a = b, x - a = b, ax = b, \frac{x}{a} = b.
- EXERCISE 15(B) — 3 questions on two-step equations.
- EXERCISE 15(C) — 27 questions mixing all forms, including negative answers and decimals.
- EXERCISE 15(D) — 10 word problems.
- Revision Exercise (Chapter 15) — 11 questions covering all forms plus word problems.
The revision exercise at the end tests everything from the chapter together. Do it last, after the four exercise blocks.
Linear Equations for Class 6 ICSE frequently asked questions
How do I solve linear equations for class 6 ICSE?
Use the four rules to keep the equation balanced. Add or subtract to remove constants, then multiply or divide to isolate the variable. Always check by substituting your answer back into the original equation.
What are the four rules for solving a linear equation?
Rule 1: add the same quantity to both sides. Rule 2: subtract the same quantity from both sides. Rule 3: multiply each term by the same quantity. Rule 4: divide each term by the same non-zero quantity.
How do I solve word problems in this chapter?
Follow the four-step method from section 15.10. Read to find what is asked, let the unknown be x, form the equation from the stated relationship, and solve it. Most problems are numbers, fractions of a number, ages, or consecutive numbers.
What is transposition in solving equations?
Transposition moves a term to the other side of the equation and changes its sign. A positive term becomes negative and a negative term becomes positive. It is a shortcut for the add-and-subtract rules.
Reference: ICSE Class 6 Mathematics textbook material, chapter 15: Simple Linear Equations — CISCE-aligned.