Properties of Equations:

Given that A, B and C represent real or complex algebraic expressions, then the following are true:

EP1 -  Addition Property of Equality: If A = B, then A + C = B + C. Note that since subtracting from both sides is the same as adding a negative amount to both sides, subtraction from both sides also is covered by this property.

EP2 -  Multiplication Property of Equality: A = B, then AC = BC.

EP3 -  Division Property of Equality: If A = B, then A/C = B/C where C≠0.

EP4 -  Absolute Value Equation Property: If |A| = B, then A = B and -A = B are both possible solutions.≠0.

EP5 -  Simple Quadratic Equations:  If A² = B, and A is unknown,  then A = +/-√B. Using this property is known as Extracting Square Roots.

EP6 -  General Quadratic Equations:  If ax² + bx + c = 0 where a, b, and c are real coefficients and x is a variable, then . This is known simply as The Quadratic Formula.  Proof is left as an exercise.

EP7 -  Radical Equations:  If √A  = B, and A is unknown,  then A = B² is an equation that when solved results in possible solutions of A. This is known as Eliminating The Radical By Squaring.

EP8 -  Rational Exponent Equations:  If A^M/N  = B, and A is unknown and M is even,  then A = +/-B^N/M is an equation that when solved results in possible solutions of A. This is known as Eliminating a Rational Exponent. This method also applies to solving nth root radical equations. For example, to solve an equation with a fourth root radical, take the 4th power of both sides.

EP9 -  Rational Exponent Equations:  If A^M/N  = B, and A is unknown and M is odd,  then A = B^N/M is an equation that when solved results in possible solutions of A.This is known as Eliminating a Rational Exponent. This method also applies to solving nth root radical equations. For example, to solve an equation with a third root radical, take the 3rd power of both sides.

EP10 - Zero Product Law: If XY = 0, then X=0 or Y=0 or both X and Y = 0.