The adhering to are the nature of equality for real numbers . Part textbooks list simply a couple of of them, others perform them all. These space the logical rules which allow you come balance, manipulate, and also solve equations.

Symmetric home

for all actual numbers x     and also   y ,

if x = y , then y = x .

order of equality does no matter.

Transitive home

for all real numbers x , y ,     and   z ,

if x = y and also y = z , climate x = z .

two numbers equal to the very same number room equal to every other.

enhancement Property

because that all actual numbers x , y ,     and   z ,

if x = y , then x + z = y + z .

these properties enable you come balance and solve equations entailing real number
Subtraction building

because that all genuine numbers x , y ,     and also   z ,

if x = y , climate x − z = y − z .

Multiplication residential or commercial property

because that all actual numbers x , y ,     and   z ,

if x = y , climate x z = y z .

department Property

because that all real numbers x , y ,     and also   z ,

if x = y , and z ≠ 0 ,

then x z = y z .

Substitution home

for all genuine numbers x     and   y ,

if x = y , climate y can be substituted for x in any type of expression.

Distributive property

for all real numbers x , y ,     and also   z ,

x ( y + z ) = x y + x z

for more, check out the ar on the distributive residential or commercial property
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