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PRE-ALGEBRA
Lesson 2-5 Warm-Up
PRE-ALGEBRA
Solving Equations by Adding and
Subtracting (2-5)
How do you
solve an
algebraic
expression?
To solve an algebraic expression, you need to isolate the variable (get the
variable alone or by itself) on one side of the equal sign. To isolate the variable
(letter), you need to work backwards, or “undo” numbers from the variable side
by doing their inverse operations (operations which “undo” each other, or
cancel each other out).
Example: x + 2 = 5
We can use a balanced scale to model this.
If we took two of the “1” weights from each
side, we would isolate the “x” weight and both
sides would remain balanced, so x = 3.
x+2 =
5
- 2
-2
x+0 =
3
PRE-ALGEBRA
Solving Equations by Adding and
Subtracting (2-5)
How do you check to
make sure the
answer to an
algebraic equation is
correct?
To check an algebraic equation, substitute (replace) the letter in the original
equation with the answer and simplify. If both sides are equal (in other
words, the substitution makes the equation a true statement), the answer is
correct.
Example: Check x + 2 = 5 for x = 3
(3) + 2 = 5
5=5 
Substitute x for 3
True Statement
What is the
Rule: Subtraction Property of Equality: If you subtract the same value
“Subtraction Property (number) from both sides of an equation (both sides are equal), the two
of Equality”?
sides of the equal sign remain equal.
If a = b, then a – c = b – c
Example: If 2 •3 = 6, then 2 •3 – 4 = 6 – 4
2
=
2
PRE-ALGEBRA
Solving Equations by Adding and
Subtracting (2-5)
What is the
“Addition Property
of Equality”?
Rule: Addition Property of Equality: If you add the same value (number) to
both sides of an equation, the two sides of the equal sign remain equal.
If a = b, then a + c = b + c
Example: If 2 •3 = 6, then 2 •3 + 4 = 6 + 4
10
Example: Solve c – 12 = 43
c – 12 = 43
+12 +12
c + 0 = 55
c
= 55
= 10 
Given
Use the Addition Property of Equality to isolate
the variable (get the c by itself)
Simplify
Identity Property of Addition
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Additional Examples
Solve y + 5 = 13.
y + 5 = 13
-5 -5
Inverse Property of Addition.
y+0 = 8
Simplify.
y
Identity Property of Addition.
= 8
Check: y + 5 = 13
(8) + 5
13
13
Replace y with 8.
= 13
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Additional Examples
Larissa wants to increase the number of books in her
collection to 327 books. She has 250 books now. Find the
number of books she needs to buy.
Words
target number
Let
Equation
x
327
is
250
plus
number to buy
= number to buy.
=
250
+
x
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Additional Examples
(continued)
327 = 250 + x
327 = x + 250
– 250
– 250
77 = x +
0
Use the Commutative Property of Addition.
Use the Inverse Property to isolate the x.
Simplify.
Larissa needs to buy 77 more books.
Check: Is the answer reasonable?
250 plus the number of books bought should be a total collection
of 327.
327 = 250 + (77)
327 =
327
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Additional Examples
Solve c – 23 = – 40.
c – 23 = – 40
+ 23
+ 23
c + 0 = –17
Add 23 to each side to isolate the c.
Identity
Simplify.Property of Addition
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Additional Examples
Marcy’s CD player cost $115 less than her DVD player.
Her CD player cost $78. How much did her DVD player cost?
Words
cost of CD player
Let
t
Equation
78
was
=
+ 115
193 = t +
less than
cost of DVD player
= cost of the DVD player.
78 = t – 115
+ 115
$115
0
t
–
115
Write an equation.
Use the Inverse Property to isolate the t.
Simplify.
Marcy’s DVD player cost $193.
PRE-ALGEBRA
Solving Equations by Adding or Subtracting
LESSON 2-5
Lesson Quiz
Solve each equation.
1. y + 8 = 12
4
2. 7 + f – 21 = –20
–6
3. 67 = g – (–36)
31
4. Ricky rides his bike 12 miles every day. He stops after 7 miles to rest.
How much farther does he have to ride?
5 mi
PRE-ALGEBRA