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 appears with power one only. 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 $x$ has an exponent of 1.
• The equation represents a straight line when graphed.
• Solutions are values of $x$ making the equation true.

In Class 8 NCERT, understanding this concept is crucial for solving problems efficiently.

Important Formulas for Solving Linear Equations

To solve linear equations in one variable, use these fundamental formulas and rules:

• Addition/Subtraction Rule: Add or subtract the same number on both sides.
• Multiplication/Division Rule: Multiply or divide both sides by the same non-zero number.

Example formulas:

1. To isolate $x$ in $ax + b = 0$:

$$x = -\frac{b}{a}$$

2. For equations like $ax + b = cx + d$:

$$x = \frac{d - b}{a - c}$$

These formulas help quickly find the solution without guesswork.

Step-by-Step Approach to Solve Linear Equations

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

1. Simplify both sides by removing brackets and combining like terms. 2. Move variable terms to one side and constants to the other. 3. Use addition or subtraction to isolate the variable term. 4. Divide or multiply to solve for the variable. 5. Verify the solution by substituting back into the original equation.

Example: Solve $3x + 5 = 2x + 9$

• Subtract $2x$ from both sides:

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

• Simplify:

$$x + 5 = 9$$

• Subtract 5:

$$x = 4$$

• Check: $3(4) + 5 = 12 + 5 = 17$ and $2(4) + 9 = 8 + 9 = 17$ (True)

Common Mistakes to Avoid While Solving Equations

Students often make these errors:

• Not performing the same operation on both sides.
• Forgetting to change the sign when moving terms across the equals sign.
• Dividing by zero or ignoring the condition $a \neq 0$.
• Skipping the verification step.

Avoid these by:

• Carefully balancing both sides.
• Writing each step clearly.
• Always checking your answer by substitution.

Comparison Table: Linear vs Non-Linear Equations

Understanding the difference helps clarify concepts:

This table helps Class 8 students focus on linear equations specifically.

Download Your Free Linear Equations in One Variable Class 8 PDF

To help your revision, download the free PDF containing:

• All important formulas
• Stepwise solved examples
• Practice questions from NCERT
• Tips for exam preparation

Having this PDF handy ensures you can revise anytime and improve problem-solving speed. Remember, consistent practice is key to mastering linear equations in one variable.