Transposition Method For Solving Linear Equations In One Variable

linear equation in one variable

Sometimes the two sides of an equation contain both variable (unknown quantity) and constants (numerals). In such cases, we first simplify two sides in their simplest forms and then transpose (shift) terms containing variable on R.H.S. to L.H.S. and constant terms on L.H.S. to R.H.S. By transposing a term from one side to the other side, we mean changing its sign and carrying it to the other side. In transposition the plus sign of the term changes into minus sign on the other side and vice-versa.

The transposition method involves the following steps :

Step1:   Clear fractions. Eliminate any fractions by multiplying both sides of the equation by a common denominator

Step2:  Simplify each side separately. Simplify each side of the equation as much as possible by using the distributive property to clear parentheses and by combining like terms as needed.

Step3:   Isolate the variable terms on one side. Use the addition property of equality to get all terms with variables on one side of the equation and all numbers on the other.

Step4:  Transform so that the coefficient of the variable is 1. Use the addition property of equality to get an equation with just the variable (with coefficient 1) on one side.

Step5:  Check. Check by substituting back into the original equation.

Step6:  Solve the equation obtained in step V by dividing both sides by the coefficient of the variable on L.H.S.

Cross-Multiplication Method for Solving Equations of the Form :