Linear Equations in One Variable Class 8 PDF: Formulas & Examples

Understanding Linear Equations in One Variable

A linear equation in one variable is an algebraic equation where the variable has a power of one. It can be written in the form:

$$ax + b = 0$$

where $a$ and $b$ are constants and $x$ is the variable. The goal is to find the value of $x$ that satisfies the equation.

Key points:

• The variable appears only once and is not multiplied by itself.
• The equation represents a straight line when graphed.
• Solutions are values of $x$ that make the equation true.

Example:

$$3x + 5 = 11$$

To solve, subtract 5 from both sides:

$$3x = 6$$

Then divide both sides by 3:

$$x = 2$$

This means $x=2$ is the solution.

Important Formulas for Solving Linear Equations

When solving linear equations in one variable, remember these key formulas and rules:

• Addition or Subtraction Property: You can add or subtract the same number on both sides.

$$ax + b = c \\ \Rightarrow ax = c - b$$

• Multiplication or Division Property: Multiply or divide both sides by the same non-zero number.

$$ax = d \\ \Rightarrow x = \frac{d}{a}$$

• Combining Like Terms: Simplify expressions by adding or subtracting terms with the same variable.

• Distributive Property: Multiply a number outside the bracket by each term inside.

$$a(b + c) = ab + ac$$

Worked Example:

Solve: $$2(x - 3) + 4 = 10$$

Step 1: Expand

$$2x - 6 + 4 = 10$$

Step 2: Simplify

$$2x - 2 = 10$$

Step 3: Add 2 to both sides

$$2x = 12$$

Step 4: Divide both sides by 2

$$x = 6$$

Step-by-Step Method to Solve Linear Equations

Follow these steps to solve any linear equation in one variable:

1. Simplify both sides: Remove brackets using distributive property and combine like terms. 2. Move variable terms to one side: Use addition or subtraction. 3. Isolate the variable: Use multiplication or division. 4. Find the solution: Calculate the value of the variable. 5. Verify the solution: Substitute back into the original equation.

Example:

Solve $$5x - 3 = 2x + 9$$

• Step 1: Move variable terms to one side:

$$5x - 2x = 9 + 3$$

$$3x = 12$$

• Step 2: Divide both sides by 3:

$$x = 4$$

• Step 3: Verify:

$$5(4) - 3 = 20 - 3 = 17$$

$$2(4) + 9 = 8 + 9 = 17$$

Both sides equal, so $x=4$ is correct.

Common Mistakes to Avoid While Solving

Students often make errors while solving linear equations. Here are some tips to avoid them:

• Not performing the same operation on both sides: Always balance the equation.
• Forgetting to change signs when moving terms: Remember to change the sign when moving terms across the equal sign.
• Ignoring brackets: Always expand brackets carefully.
• Dividing by zero: Never divide by zero; check the coefficient.
• Not verifying the solution: Always substitute the answer back.

Comparison Table:

How to Use the Linear Equations in One Variable Class 8 PDF Effectively

The NCERT Class 8 linear equations PDF is a valuable resource for mastering this chapter. Here’s how to use it well:

• Start with theory: Read definitions and properties carefully.
• Learn formulas: Memorize key formulas for quick recall.
• Practice solved examples: Understand step-by-step solutions.
• Attempt exercises: Solve all questions at the end of the chapter.
• Revise regularly: Use the PDF for quick revision before exams.

Benefits:

• Portable and easy to access anytime.
• Contains all formulas and examples in one place.
• Helps build confidence through practice.

Download the PDF and keep it handy for daily practice and revision.

Tips to Score Well in Class 8 Mathematics Exams

To excel in the linear equations chapter and overall Class 8 Maths:

• Understand concepts, don’t just memorize.
• Practice NCERT questions thoroughly.
• Solve additional problems to strengthen skills.
• Manage time well during exams.
• Write neat and stepwise solutions.
• Revise formulas and key points regularly.

Remember, consistent practice with the linear equations in one variable class 8 PDF will improve your problem-solving speed and accuracy.