CLASS-6
SOLVING LINEAR EQUATION IN ONE VARIABLE 

SOLVING LINEAR EQUATION IN ONE VARIABLE -

Solving a linear equation in one variable is a straight forward process. A linear equation in one variable typically has the form:

   ax + b = c

 Where:-

  • x is the variable you're trying to solve for.
  • a, b, and c are constants, with a not equal to zero.

To solve for x, follow these steps:-

  1. Isolate the Variable x:-  First, move the constant term (b) to the other side of the equation by subtracting it from both sides. This step is also known as "transposing" or "moving terms."The equation becomes   ax = c − b.
  2. Solve for x:- Divide both sides of the equation by the coefficient of x, which is a. This will isolate x.The equation becomes x = (c − b)/a​.
  3. Calculate the Value of x:-  Simply plug in the values of a, b, and c into the equation and perform the arithmetic operations to find the value of x.

Here's an example to illustrate the process:

Example.1)

       Linear Equation:-   3x + 5 = 11

       Solution:-

  1. Isolate the variable x by moving the constant term to the other side:-          3x = 11 − 5 

             3x = 6

  1. Solve for x by dividing both sides by the coefficient of x = 3:- 

             3x = 6

            3x/3 = 6/3

             x = 2

So, the solution to the equation is x = 2.      (Ans.)

Algebra

Example.2) Solve for x:

            3x − 5 = 16

  1. Isolate the Variable:-  Move the constant term (-5) to the other side by adding 5 to both sides: 3x = 16 + 5,  3x = 21
  2. Perform Necessary Operations:- To isolate x, divide both sides by the coefficient of x, which is 3:-  3x = 21​
  3. Simplify and Solve for the Variable:- Simplify the right side of the equation: x = 7
  4. Check Your Solution:- Substitute x = 7 back into the original equation:- 3(7) − 5 = 21 − 5 = 16       

The equation is satisfied, so the solution is x = 7.

This is a basic example, but the same principles apply to more complex linear equations in one variable. The key is to isolate the variable and perform the necessary operations to find its value.

Algebra