# Exercise 2.1 class 8 solution

### Exercise 2.1 class 8 solutions-Equation in one variable

An equation in one variable is a mathematical expression that contains one variable (usually represented by a letter like x) and equates it to a value or another expression. The goal is typically to find the value of the variable that satisfies the equation. Equations in one variable can take various forms, but here are a few common examples:

1. Linear Equation: A linear equation in one variable is of the form ax + b = 0, where “a” and “b” are constants. For example, 3x – 5 = 7 is a linear equation in one variable. The goal is to solve for x to find the value that makes the equation true.
2. Quadratic Equation: A quadratic equation in one variable is of the form ax^2 + bx + c = 0, where “a,” “b,” and “c” are constants. For example, x^2 – 4x + 4 = 0 is a quadratic equation in one variable. To solve it, you typically use the quadratic formula or factoring.

### Exercise 2.1 class 8 solutions-linear equation in one variable

A linear equation in one variable is a type of equation where the variable is raised to the first power and is not multiplied or divided by any other variables. These equations have the form:

ax + b = 0

In this equation:

• “x” represents the variable you’re trying to solve for.
• “a” and “b” are constants (real numbers) where “a” cannot be equal to zero because dividing by zero is undefined.

The goal when dealing with linear equations in one variable is to find the value of “x” that satisfies the equation. To solve such an equation, you typically perform the following steps:

1. Isolate the variable “x” on one side of the equation. You do this by performing algebraic operations to move all “x” terms to one side and constants to the other side of the equation. For example, if you have the equation 2x + 3 = 7, you can isolate “x” by subtracting 3 from both sides, resulting in 2x = 4.
2. Solve for “x.” In this step, you divide both sides of the equation by the coefficient of “x” (in this case, 2) to obtain the value of “x.” In our example, 2x = 4 becomes x = 2.

So, in the linear equation 2x + 3 = 7, the solution is x = 2.

Linear equations in one variable are fundamental in algebra and are used in various real-life situations to solve for unknown values, such as in calculating distances, costs, and many other scenarios.

### Exercise 2.1 class 8 solution –

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##### Exercise 2.1 class 8 solution -Solving equation having variables on both side

Solving equations with variables on both sides involves moving the variables to one side and the constants to the other side in order to isolate the variable you’re trying to solve for. The key steps for solving such equations are as follows:

Step 1: Distribute (if necessary)

If the equation contains parentheses or requires distributing, do so to simplify the equation.

Step 2: Get the Variables on One Side

a. Start by moving one of the variable terms to the other side of the equation. You can do this by adding or subtracting the same term to both sides.

b. Your goal is to have all variable terms on one side of the equation and constants on the other side. This will leave you with an equation of the form “ax = b.”

Step 3: Combine Like Terms

Combine any like terms on both sides of the equation. This simplifies the equation.

Step 4: Isolate the Variable

a. Divide both sides of the equation by the coefficient of the variable term (the “a” in “ax = b”). This will isolate the variable on one side.

b. If you’re dealing with fractions, you can multiply both sides of the equation by the reciprocal of the fraction to eliminate it.

Step 5: Solve for the Variable

You should now have a simplified equation with the variable on

one side. Solve for the variable to find its value.

Here’s an example:

Let’s solve the equation with variables on both sides:

3x – 4 = 2x + 7

Step 1: There is no need to distribute or simplify further.

Step 2: Move the variable terms to one side:

3x – 2x = 7 + 4

x = 11

So, the solution to the equation is x = 11.

Exercise 2.1 class 8 solution are provided here to help students .so they can clear their doubt regarding this exercise.hope students will like our efforts of providing help by providing Exercise 2.1 class 8 solution .