I. Write an expression to represent the following situation:
Tim got a DVD burner for his computer on his birthday. He was able to create 3 DVD's out of the movies he'd copied from his movie collection with 6 movies left over. If x represents the amount of movies each DVD holds write an expression for the total amount of movies . 3x
+
6
1
After a month Tim burned 6 more DVD's with 2 movies left over. What algebraic expression could be used for this situation?
6x
2
+
How would you represent the total amount of movies in his collection?
3x
+
6
+
6x
+
2
= 9x
+
8
Only like terms can be added or subtracted!
In the expression: 4x + 2y + 3
4x, 2y and 3 are called the ________
TERMS
4 and 2 are the ______________ of the variables x
and y.
COEFFICIENTS
3 is referred to as a ____________
CONSTANT
2
YOUR TURN:
Given the expression 3x2 + 5x – 4, name the following:
2
The terms of the expression: _____, _____
3x 5 x and ____
4
The coefficient of x: ___
5
The coefficient of x2: ____
3
The constant: ____
4
Properties of Numbers
Commutative Property: For all numbers a, b and c:
a
4   3 x  2  4   ___+3x
2

Associative Property: For all numbers a, b and c:
4   3x  2    __
4  2   3x
 ___
6  3x
3
Distributive Property: For all numbers a, b and c:
a ( b + c) = ab + ac
Example 1: (4x + 6x) = ( 4 + 6 ) x
= 10x
Example 2: 3(x + 2) = 3x + 6
Using the Properties of Numbers, simplify the following expressions:
1.)  5a  2   3a  6 
Rewrite:
5a  2  3a  6
Regroup:
5a  3a    2  6
Answer:
8a  8
4
2.)  2a  3b  5c    7a  3b  5c 
Rewrite:
Regroup:
Answer:
2a  3b  5c  7a  3b  5c
 2a  7a   3b  3b   5c  5c 
9a  10c
3.)  x  y  z    2w  3 y  5
Rewrite:
Regroup:
Answer:
x  y  z  2w  3 y  5
x   y  3 y   z  2w  5
x  4 y  z  2w  5
5
1
 1

4.)  x  1   x 1
2
 3

1
1
x  1  x 1
2
3
Rewrite:
Regroup:
1
1 
 x  x   1 1
3 
2
Answer:
5
x
6
 5) Write an algebraic expression for the perimeter of the triangle and then simplify:
3x + 2
2x + 8
2 x  8  3x  2  6 x  3
6x - 3
 2 x  3x  6 x   8  2  3
P = 11x  7
6
Homework : Section 5.1
pages 277‐279
#’s 8‐38 EVEN 7