Example of Linear Equations:
Solve the equation 2x + 9 = 3(x + 4).
Solution:
Step 1. Using Axiom 2, subtract 3x and 9 from both sides of the equation.
2x + 9 = 3(x + 4)
2x + 9 - 3x - 9 = 3x + 12 - 3x - 9
-x = 3
Step 2. Using Axiom 4, divide both sides of the equation by -1.
-x/-1 = =3/-1
x = -3
Step 3. Check the root.
2(-3) + 9 = -6 + 9 = 3
3[(-3) + 4] = 3(1) = 3
The root checks.
These similar steps can be used to solve equations which involve various unknowns. The result is an expression for one of the unknowns in terms of the other unknowns. This is particularly significant in solving practical problems. Frequent the known relationship between various physical quantities must be rearranged in sequence to solve for the unknown quantity. The steps are performed so in which the unknown quantity is isolated on the left-hand side of the equation.