Equations having one variable and the degree of the variable being one are known as linear equations in one variable. Standard form of a linear equation in two variables is,
Where a and b are real numbers, and both a and b are not equal to zero. Every linear equation in one variable has a unique solution.
Both side of the equation are considered to be balanced for solving equations. Equality sign denotes that the expressions on either side of the ‘equal to’ sign are equal. Since the equation is balanced, for solving it same mathematical operations are performed on both sides of the equation in a manner that it does not affect the balance of the equation. 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 shift the variables from one side of the equality to the other side of the equality. In the method of transposition, the operation on the operand gets reversed.
In the equation 5x – 9 = -3x + 19, we transpose -3x from the left hand side to the right 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 the equation 5x – 9 = -3x + 19, we will get 9 = 9, thereby satisfying the equality and giving us the required solution.
Click here to read about the application of linear equations.
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