Download Lesson 2.5

Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
(For help, go to Lesson 2-1.)
Bell Work # 9
Simplify each expression.
1. 3 + 4 – 4
2. 7 + 9 – 7
3. 8 – 2 + 2
4. 6 + 2 – 2
Check Skills You’ll Need
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solutions
1. 3 + 4 – 4
= 3 + (4 – 4)
=3+0
=3
2. 7 + 9 – 7
= 9 + (7 – 7)
=9+0
=9
3. 8 – 2 + 2
= 8 + (2 – 2)
=8+0
=8
4. 6 + 2 – 2
= 6 + (2 – 2)
=6+0
=6
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Vocabulary
Vocabulary and Concepts
Subtraction Property of Equality
You can subtract the same number from each side of an equation
Arithmetic
10 = 2( 5 )
5
10 – 5 = 2( 5 ) - _____
Algebra
if a = b
c
then a – c = b - _____
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Vocabulary
Addition Property of Equality
You can add the same number from each side of an equation
Arithmetic
8 = 2( 4 )
3
8 + 3 = 2( 4 ) + _____
Algebra
if a = b
then a + c = b + c_____
Inverse Operations
____________________
are operations that undo each other
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve y + 5 = 13.
Method 1
Method 2
y + 5 = 13
y + 5 – 5 = 13 – 5
y=8
Subtract 5
y + 5 = 13
from each side.
Simplify.
–5=–5
y=
8
Check y + 5 = 13
8 + 5 13
Replace y with 8.
13 = 13
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
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
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+
x
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
(continued)
327 = 250 + x
327 = x + 250
327 – 250 = x + 250 – 250
77 = x
Use the Commutative Property of Addition.
Subtract 250 from each side.
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.
250 + 77 = 327
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve c – 23 = – 40.
c – 23 = – 40
c – 23 + 23 = – 40 + 23
c = –17
Add 23 to each side.
Simplify.
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Marcy’s CD player cost $113 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
was
$113
less than
cost of DVD player
= cost of the DVD player.
80
=
t
–
110
80 = t – 110
80 + 110 = t – 110 + 110
190 = t
Add 110 to each side.
Simplify.
Marcy’s DVD player cost $190.
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve each equation.
2. 7 + f – 21 = –20
1. y + 8 = 12
–6
4
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
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