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 algebraic equation in which the variable appears with power one only. It can be written in the form:

$$ax + b = 0$$

Here, $x$ is the variable, $a$ and $b$ are constants, and $a \neq 0$. The equation represents a straight line when graphed on a coordinate plane. For example:

• $3x + 5 = 0$
• $-2x + 7 = 0$

These equations have exactly one solution, which can be found by isolating $x$.

Basic Components of a Linear Equation

Understanding the parts of a linear equation helps in solving it easily:

• Variable ($x$): The unknown quantity to find.
• Coefficient ($a$): The number multiplying the variable.
• Constant ($b$): A fixed number without a variable.

For example, in the equation $4x - 9 = 0$:

• Variable: $x$
• Coefficient: 4
• Constant: -9

Knowing these terms helps you perform operations correctly.

Steps to Solve Linear Equations in One Variable

Solving linear equations involves isolating the variable on one side. Follow these steps:

1. Simplify both sides by removing brackets and combining like terms. 2. Move variable terms to one side and constants to the other. 3. Perform inverse operations (addition, subtraction, multiplication, division) to isolate the variable. 4. Check the solution by substituting it back into the original equation.

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

• Step 1: Bring variables to one side: $5x - 2x = 9 + 3$
• Step 2: Simplify: $3x = 12$
• Step 3: Divide both sides by 3: $x = 4$
• Step 4: Verify by substitution.

Real-Life Applications of Linear Equations

Linear equations in one variable help solve many practical problems, such as:

• Calculating expenses and budgets
• Finding unknown quantities in word problems
• Distributing items equally
• Determining speed, time, and distance relationships

For example, if a book costs ₹x and you buy 3 books for ₹150, the equation is:

$$3x = 150$$

Solving gives $x = 50$, the price of one book.

Comparison: Linear Equations vs Other Equations

Here's how linear equations in one variable compare with other types of equations:

This helps you identify and solve equations correctly.

Important Formulas and Tips for Class 8 Students

Keep these formulas and tips in mind:

• General form: $$ax + b = 0$$
• Solution: $$x = \frac{-b}{a}$$
• Always perform the same operation on both sides.
• Check your answers by substitution.
• Remember, $a \neq 0$; otherwise, it's not a linear equation.

Quick Tip: When variables appear on both sides, bring them to one side before solving.