Properties of Equality

NOTE:

Some second-degree equations will be encountered in the pH and buffers

problems. However, methods taught here will be sufficient for any problem

solving.

1-10. PROPERTIES OF EQUALITY

For any real number a, b, or c, the properties are as follows.

a. Reflexive Property.

a=a

Example: 8 = 8

b. Symmetric Property.

If a = b, then b = a

Example: If x + 5 = y, then y = x + 5

c. Transitive Property.

If a = b and b = c, then a = c

Example: If a + b = c, and c = 3a, then a + b = 3a

d. Substitution Property.

If k = x, then k may replace x in any equation without changing the truth of the

equation.

Example: If 2k - 4 = x, and x + k = 9,

then 2k - 4 + k = 9

1-11. RULES OF EQUALITY

a. Adding or subtracting the same quantity on both sides of an equation

produces an equivalent equation.

b. Multiplying or dividing both sides of an equation by the same nonzero quantity

produces an equivalent equation.

c. Simplifying an expression on either side of an equation produces an

equivalent equation.

MD0837

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