INTRODUCTION CLASS 8 MATHS CHAPTER 2 LINEAR EQUATION IN ONE VARIABLE #MATH #CLASS8 #NCERT

Chapter 2 of Class 8 Math usually covers **Linear Equations in One Variable**. Here's a comprehensive introduction to this topic: *Introduction to Linear Equations in One Variable* *1. What is a Linear Equation in One Variable?* A linear equation in one variable is an equation that can be written in the form: \[ ax + b = 0 \] where: \(a\) and \(b\) are constants. \(x\) is the variable. In this equation: \(a\) is the coefficient of \(x\). \(b\) is a constant term. *2. General Form:* The general form of a linear equation in one variable can also be written as: \[ ax + b = c \] where \(c\) is another constant. This can be rearranged into the standard form \(ax + b = 0\) by subtracting \(c\) from both sides: \[ ax + b - c = 0 \] *3. Solving Linear Equations:* To solve a linear equation in one variable, you need to find the value of \(x\) that makes the equation true. This involves isolating \(x\) on one side of the equation. Here are the steps: 1. *Simplify the Equation:* Combine like terms on both sides if necessary. 2. *Isolate the Variable:* Use arithmetic operations to isolate \(x\). This often involves adding or subtracting constants and then dividing or multiplying by the coefficient of \(x\). *4. Example:* Solve the equation: \[ 3x + 5 = 14 \] *Step 1: Subtract 5 from both sides to isolate the term with \(x\):* \[ 3x + 5 - 5 = 14 - 5 \] \[ 3x = 9 \] *Step 2: Divide both sides by 3 to solve for \(x\):* \[ \frac{3x}{3} = \frac{9}{3} \] \[ x = 3 \] So, the solution is \(x = 3\). *5. Types of Linear Equations:* *Simple Linear Equations:* Involve straightforward terms like \(ax + b = c\). *Equations with Variables on Both Sides:* For example, \(2x + 3 = x + 7\). To solve, collect all \(x\) terms on one side and constants on the other. *Equations with Fractions:* For example, \(\frac{2x}{3} + 5 = 7\). Solve by eliminating the fraction first. *6. Checking Solutions:* After solving a linear equation, it's important to check the solution by substituting it back into the original equation to ensure that both sides are equal. *7. Real-World Applications:* Linear equations in one variable are used to solve problems involving: *Budgeting:* Determining how much money is left after purchases. *Distance, Speed, and Time:* Calculating time or distance based on known speeds and distances. *Mixtures:* Finding the proportions of different substances in a mixture. *8. Example of Real-World Problem:* A person buys 5 pens and 3 notebooks for $23. If the price of a pen is $2, find the price of a notebook. Let \( x \) be the price of a notebook. The equation is: \[ 5 \times 2 + 3x = 23 \] \[ 10 + 3x = 23 \] Subtract 10 from both sides: \[ 3x = 13 \] Divide both sides by 3: \[ x = \frac{13}{3} \approx 4.33 \] So, the price of a notebook is approximately $4.33. Linear equations in one variable are foundational for more advanced algebraic concepts and are widely used in various practical applications.#easytounderstandmath #maths #english #ALL CLASSES #MATHSCHAPTER1 #CHAPTER3 #WHOLENUMBER #RATIONALNUMBER #REALNUMBER #INTERGERS #DIVIDE #SUM #MULTIPLY #POLYNOMIAL #DECIMAL #PLACEVALUE #TRIANGLES #SPHARE ##HAS HAVE HAD #WAS WERE #WILL SHALL GRAMMER BASIC ENGLISH SPKENENGLISH HOWTOSPEAKENGLISH ENGLISHFORALLCLASEES Enter comma-separated values314/500