Linear Equations:

These four axioms are used to solve the linear equations with three steps:

Step 1. Using the addition and subtraction axioms, Axioms 1 and 2, eliminate all terms along with no unknowns from the left-hand side of the equation and eliminate all terms with the unknowns from the right-hand side of the equation.

Step 2. Using   the   multiplication   and   division   axioms, Axioms 3 and 4, eliminate an coefficient from the unknowns on the left-hand side of the equation.

Step 3. Check the root through substituting it for the unknowns within the original equation.

Example 1:

Solve the equation 3x + 7 = 13.

Solution:

Step 1. Using Axiom 2, subtract 7 from both sides of the equation.

3x + 7 - 7 = 13 - 7

3x = 6

Step 2. Using Axiom 4, divide both sides of the equation by 3.

3x/3 = 6/3

x=2

Step 3. Check the root.

3(2) + 7 = 6 + 7 = 13

The root checks.