Page 56 - CalcBus_Flipbook

6-6 Equations and Formulas CH 6]

The Equation Scale

In order to balance the scale again, 2 ounces MUST be added to the left
6oz 6oz side of the scale.

In this way, the balance of the scale has been maintained by adding
the same amount to each side of the scale.

SCALE IS BALANCED
Left Side = Right Side

———————— Rule to Remember —————————
1. To keep the balance needed in an equation, anything added to one side MUST also be
added to the other side.
2. Anything subtracted from one side of an equation MUST also be subtracted from the
other side.
3. If one side of an equation is multiplied by a number, the other side MUST be multiplied
by the same number.
4. If one side of an equation is divided by a number, the other side MUST be divided by the
same number.

To solve an equation is to find those values of the literal quantity, or unknown, which will make
the statement of equality true. The value or values of the unknown which balance an equation are
called roots. In the equation 2y = 12, 6 is the root. If a root is substituted for the unknown quantity
(y) in an equation, and the equation is then balanced, the root is said to satisfy the equation. When this
is done, the answer is checked.

Example A: Determine if y + 1 = 12 is an identity or a conditional equation.

Solution: 11 added to 1 is 12. Since there are no other possible answers, y + 1 = 12 is said to be a
conditional equation.

y + 1 = 12 Objective: get y alone on one side of the equation.
y + 1 – 1 = 12 – 1 Add the opposite to both sides of the equation, maintain equality.
y + 0 = 11
y = 11

Example B: Determine if 2 is a root of 3y + 4 = 10. Does the value 2 solve the equation?
Solution: If 2 is a root of 3y + 4 = 10, then if 2 is substituted for y in the equation, the left member
will be equal to the right member.

3y + 4 = 10 Objective: test the root value 2 for the equation.
3(2) + 4 = 10 substitute 2 for the variable y and the relationship is multiplication.
6 + 4 = 10
10 = 10

Since the left member of the equation is equal to the right member, 2 is a root of 3x + 4 = 10.

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