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CH 6] Calculating Business 6-5

convert degrees Celsius to degrees Fahrenheit. The letters “F” and “C” are variables and can change
in value, whereas the fraction 9/5 and 32 are constants and do not vary in value. The expressions on
either side of the = sign are called members of the equation.

Members of the equation

F = 9/5C + 32
In an equation the letter whose value must be found is called the unknown number or the
unknown. These are also equations:

y = 10 x + 6 = 14 c – 10 = 5

In the equation x + 6 = 14, x + 6 is called the left member of the equation and 14 is the right
member. The equation x + 6 = 14 means that 6 added to an unknown number equals 14.

Conditional and Identical Equations
There are two types of equations: conditional equations and identical equations.
1. A conditional equation, usually simply called an equation, is not true for all values
of the unknown. It is true only for a limited number of values of the literal
quantity. For example,
2Y = 12 is true only when Y = 6.
The mathematical relationship in 2Y is one of multiplication and could be expressed as:
2  Y (2)(Y) 2 x Y
In this work, unless told otherwise, when referring to an equation, the equation referred to is always a
conditional equation.

2. An identical equation or identity, is true for all values of the unknown. For
example, 2y + 3y = 5y is true when y = 1, 2, 3, 5,… 60,… 1000, or any other
number.

Solving an Equation
The two members of an equation balance each other just as do the opposite sides of a balance
pair of scales; each side of the = sign MUST be equal and when calculated, are the same value. This is
best expressed as “one side MUST equal the other side” and “the equality of the equation MUST be 6
maintained.” Therefore, if a change is made in one member (side) of an
equation, the same or an equaling change MUST be made in the other The Equation Scale
member to keep the balance.

Suppose you have a balance scale with 4 ounces on each side.
4oz 4oz
The scale is balanced.
The Equation Scale

SCALE IS BALANCED
4oz Left Side = Right Side

6oz Now suppose 2 ounces are added to the right side of the scale. The scale
will then be unbalanced.

SCALE OUT OF BALANCE
Left Side ≠ Right Side

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