4 +
x
= 12
Original equation.
4 +
x
−
4 = 12
−
4
Subtract 4 from both sides of the equation.
x
= 8
On the left, subtracting 4 “undoes” the effect
of adding 4 and returns
x
. On the right,
12
−
4 = 8.
4.
Answer the Question.
The number is 8.
5.
Look Back.
Does the solution 8 satisfy the words in the original problem?
We were told that “four more than a certain number is 12.” Well, four
more than 8 is 12, so our solution is correct.
Answer:
7
You Try It!
EXAMPLE 8.
Amelie withdraws $125 from her savings account. Because of
Fred withdraws $230 from
his account, lowering his
balance to $3,500. What was
his original balance?
the withdrawal, the current balance in her account is now $1,200. What was
the original balance in the account before the withdrawal?
Solution.
In our solution, we will carefully address each step of the
Require-
ments for Word Problem Solutions
.

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1.6.
SOLVING EQUATIONS BY ADDITION AND SUBTRACTION
83
1.
Set up a Variable Dictionary.
We can satisfy this requirement by simply
stating “Let
B
represent the original balance in Amelie’s account.”
2.
Set up an Equation.
We can describe the situation in words and symbols.
Original
Balance
minus
Amelie’s
Withdrawal
is
Current
Balance
B
−
125
=
1200
3.
Solve the Equation
. To “undo” the subtraction, add 125 to both sides of
the equation.
B
−
125 = 1200
Original equation.
B
−
125 + 125 = 1200 + 125
Add 125 to both sides of the equation.
B
= 1325
On the left, adding 125 “undoes” the effect
of subtracting 125 and returns
B
. On the right,
1200+125=1325.
4.
Answer the Question.
The original balance was $1,325.
5.
Look Back.
Does the solution $1,325 satisfy the words in the original
problem? Note that if Amelie withdraws $125 from this balance, the new
balance will be $1,200. Hence, the solution is correct.
Answer:
$3,730.
You Try It!
EXAMPLE 9.
The perimeter of a triangle is 114 feet. Two of the sides of
The perimeter of a
quadrilater is 200 meters. If
three of the sides measure 20,
40, and 60 meters, what is
the length of the fourth side?
the triangle measure 30 feet and 40 feet, respectively. Find the measure of the
third side of the triangle.
Solution.
In our solution, we will carefully address each step of the
Require-
ments for Word Problem Solutions.
1.
Set up a Variable Dictionary.
When geometry is involved, we can cre-
ate our variable dictionary by labeling a carefully constructed diagram.
With this thought in mind, we draw a triangle, then label its known and
unknown sides and its perimeter.

84
CHAPTER 1.
THE WHOLE NUMBERS
x
30 ft
40 ft
Perimeter = 114 ft
The figure makes it clear that
x
represents the length of the unknown
side of the triangle. The figure also summarizes information needed for
the solution.
2.
Set up an equation.
We know that the perimeter of a triangle is found
by finding the sum of its three sides; in words and symbols,
Perimeter
is
First
Side
plus
Second
Side
plus
Third
Side
114
=
x
+
30
+
40
Simplify the right-hand side by adding 30 and 40; i.e., 30 + 40 = 70.