Page 80 - Algebra 1

c. d+(e+f)=(d+e)+f
SOLUTION Substitute a value for the variables to determine whether the
statement is true.
Let d = 5, e = 7, and f = 9. 5 + (7 + 9) (5 + 7) + 9 5+16 12+9
21=21 ✓
The statement is true by the Associative Property of Addition.
Justifying Steps to Simplify an Expression
Simplify each expression. Justify each step.
Example
3
a. 16+3x+4 SOLUTION
16 + 3x + 4
= 3x + 16 + 4 = 3x + (16 + 4) = 3x + 20
_1 b. (25)·y·(25)
SOLUTION
() _1 25 ·y·(25)
Caution
Don’t skip or combine steps. For each property necessary to simplify the expression, a step must be shown.
( ) _1
Commutative Property of Addition Associative Property of Addition Add.
Commutative Property of Multiplication
Multiply
Identity Property of Multiplication
Application: Consumer Math
= 25 = 1 · y
· (25 )· y
= y
Example
4
Envelopes, pens, and correction tape can be purchased at an office supply store for the following prices respectively: $2.85, $5.35, and $2.15. Find the total cost of the supplies. Justify each step.
SOLUTION
$2.85 + $5.35 + $2.15
= $2.85 + $2.15 + $5.35 = ($2.85 + $2.15) + $5.35 = $5.00 + $5.35
= $10.35
The supplies will cost $10.35.
Commutative Property of Addition Associative Property of Addition Add within the parentheses.
Add.
Lesson 12 65