Standard Form
The standard form of a linear equation with one variable is:
ax + b = 0.
Where ‘a’ and ‘b’ are the real numbers.
Both ‘a’ and ‘b’ are not equal to zero.
Thus, the linear equation formula in one variable is ax + b = 0.
The procedures below are used to solve an equation with only one variable.
Step 1: Remove any fractions using LCM.
Step 2: Simplify the complexity of both sides of the equation.
Step 3: Isolate the variable.
Step 4: Verify your solution.
Example
Let us understand the concept with the help of an example.
For solving equations with variables on both sides, the following steps are followed:
Consider the equation: 5x – 9 = -3x + 19
Step 1: Transpose all the variables on one side of the equation. By transpose, we mean to shift the variables from one side of the equation to the other side of the equation. In the method of transposition, the operation on the operand gets reversed.
In equation 5x – 9 = -3x + 19, we transpose -3x from the right-hand side to the left-hand side of the equality, the operation gets reversed upon transposition and the equation becomes:
5x – 9 +3x = 19
⇒ 8x – 9 = 19
Step 2: Similarly transpose all the constant terms on the other side of the equation as below:
8x -9 = 19
⇒ 8x = 19 + 9
⇒ 8x = 28
Step 3: Divide the equation with 8 on both sides of the equality.
8x/8 = 28/8
⇒ x = 28/8
If we substitute x = 28/8 in equation 5x – 9 = -3x + 19, we will get 9 = 9, thereby satisfying the equality and giving us the required solution.