Solve the linear equation:

The equation relating the pressure that is denoted by P, to the force, F & the area, A, over which the force is applied is P =F/A.  Solve this equation for F, in terms of P and A.

Solution:

Step 1. Axioms 1 and 2 do not help solve the problem, so go to Step 2.

Step 2. Using Axiom 3, multiply both sides of the equation by A.

P (A) =  F/A (A)

F = PA

Step 3. Check the root.

 PA/A = P

The root checks.

The addition or subtraction of the similar quantity from both sides of an equation may be accomplished through transposing a quantity from one side of the equation to another.  Transposing is a shortened way of applying the addition/subtraction axioms.  Any term may be transposed/transferred from one side of an equation to the other if its sign is changed.   Therefore, in the equation 5x + 4 = 7, the 4 can be transposed to the other side of the equation through changing its sign.  The output is 5x = 7 - 4 or 5x = 3.  This corresponds to applying the subtraction axiom, Axiom 2 and subtracting 4 from both sides of the equation.