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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.
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