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Algebra: Isolate The Variable (Transposition)

Transposition is a method to isolate the variable to one side of the equation and everything else to the other side so that you can solve the equation.

Two methods are covered here:

Method 1 (as is usually taught in schools) and

Method 2 (a shortcut that allows you to work faster)

Method 1

A quick review of the basic principles - all equations have two sides: a Left Side (LS) and a Right Side (RS). The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolate the variable (or the unknown quantity).

For example:

5x + 8 = 3x – 6

We want to get rid of the number 8 from the left side.
So we subtract 8 from both sides of the equation.

5x + 8	=	3x – 6	original equation
– 8	=	– 8	subtract 8 from both sides
5x	=	3x – 14	resulting equation

Next, we want to get rid of 3x from the right side.
So, we subtract 3x from both sides of the equation.

5x	=	3x – 14	result from above
– 3x	=	– 3x	subtract 3x from both sides
2x	=	– 14	resulting equation

Now, we want to get rid of the coefficient 2.
So, we divide 2 from both sides of the equation.

2x	=	– 14	result from above
÷2	=	÷2	divide both sides by 2
x	=	– 7	resulting solution

Have a look at this video that clearly explains the steps to isolate a variable and solve linear eqautions.

Method 2

In this method we isolate the variable by moving like terms to one side of the equation. To maintain the equality of both sides, there are two rules for Method 2.
When moving a term to the other side of the equal sign: