The general form of a linear equation is
, 
.To solve an equation for the indicated variable means to algebraically manipulate
the numbers, symbols, and variables in the equation so that finally we have the
indicated variable alone on side side of the equation and everything else -
all other numbers, symbols, and variables - on the other side of the equation.
To solve a linear equation, we must perform the four basic operations of addition,
subtraction, multiplication, and division on both sides of the equation until the indicated
variable is isolated on one side of the equation.
Solve the above equation for
:We must isolate
on one side of the equation. Which side is irrelevant, we will get the same correct answer.
To be specific, isolate
on
the left side of the equation.Get rid of
by
subtracting it from both side of the equation,
or
.Now we want to cancel the factor
in the product 
.The only way to cancel a factor in a product is to divide it away.
So we divide both sides of the equation by
or, equivalently, we multiply both sides of the equation by
.
Finished !
This process enables us to solve any linear equation.