What is Linear Equations in One Variable Class 8: Definition & Examples

Definition of Linear Equations in One Variable

A linear equation in one variable is an equation that can be written in the form:

$$ax + b = 0$$

where:

• $x$ is the variable
• $a$ and $b$ are constants with $a \neq 0$

The variable $x$ appears only to the first power (degree one). This means the equation graphs as a straight line if plotted. For example:

• $3x + 5 = 0$
• $7 - 2x = 0$

are linear equations in one variable.

In Class 8 NCERT Mathematics, understanding this definition is crucial as it forms the base for solving algebraic problems.

How to Identify Linear Equations in One Variable

To identify if an equation is a linear equation in one variable, check the following:

• The equation contains only one variable (like $x$).
• The variable is raised to the power 1 (no squares, cubes, or roots).
• The equation can be simplified to the form $ax + b = 0$.

Examples:

Remember, only one variable with degree one makes it a linear equation in one variable.

Methods to Solve Linear Equations in One Variable

Solving linear equations in one variable means finding the value of the variable that makes the equation true. Follow these steps:

1. Simplify both sides: Remove brackets and combine like terms. 2. Bring variable terms to one side: Use addition or subtraction. 3. Isolate the variable: Use multiplication or division. 4. Check the solution: Substitute the value back into the original equation.

Example 1: Solve $3x + 5 = 11$

• Subtract 5 from both sides:

$$3x + 5 - 5 = 11 - 5$$ $$3x = 6$$

• Divide both sides by 3:

$$x = \frac{6}{3} = 2$$

• Check by substituting $x=2$:

$$3(2) + 5 = 6 + 5 = 11$$ (True)

Example 2: Solve $7 - 2x = 1$

• Subtract 7 from both sides:

$$7 - 2x - 7 = 1 - 7$$ $$-2x = -6$$

• Divide both sides by -2:

$$x = \frac{-6}{-2} = 3$$

• Check by substituting $x=3$:

$$7 - 2(3) = 7 - 6 = 1$$ (True)

These steps ensure you solve equations correctly every time.

Applications of Linear Equations in One Variable

Linear equations in one variable are used in many real-life situations and other math topics. Some common applications include:

• Solving word problems: Calculating ages, distances, or costs.
• Geometry: Finding unknown lengths or angles.
• Finance: Calculating profit, loss, or discounts.
• Science: Relating quantities in experiments.

Example:

If the sum of a number and 9 is 20, find the number.

• Let the number be $x$.
• Equation: $x + 9 = 20$
• Subtract 9: $x = 20 - 9 = 11$

So, the number is 11.

Understanding linear equations helps solve such practical problems quickly and accurately.

Tips and Tricks for Class 8 Students to Master Linear Equations

Here are some helpful tips for Class 8 students studying linear equations in one variable:

• Practice regularly: Solve different types of equations daily.
• Understand each step: Don’t just memorize; know why you perform each operation.
• Use balance method: Whatever you do to one side, do to the other.
• Check answers: Always substitute your solution back into the original equation.
• Break complex problems: Simplify terms before solving.

By following these tips, you can improve speed and accuracy in exams.