Download Algebra P3

Algebra P3
Notes for 5-#1
Name: ___________________________
August 22-23, 2013
Period: _____
ORDER OF OPERATIONS
The rules, in order are:
 Do operations within parentheses first.
 Next, perform operations with exponents
 Then do multiplication and division from left to right
 Then do addition and subtraction in order from left to right.
Examples: Simplify the expressions. Show all work vertically completing only one operation per step.
3
a) 4(5)2  4  5(8)  10
b) 3  5(1  4)2
c) 5  2  6  8
3  5

3  5 
2
3  ___
____
Evaluate each expression by substituting in the value and simplifying.
1
b) 3x2  4 x  5, x  3
a) x 2  5 x  1, x 
c)
2
3
3   4    5
3
4 x  2 y  3 y 2 , x  3 y  2
4
    5
  2    3 
2
____  ____  5
____  5
____
Examples: Solve the following equations. Check your solution.
a) 5x  2  3x  14
b) 3x  5  12 x  32
Check:
Check:
c)
16a  12  8  11a
Check:
DISTRIBUTIVE PROPERTY
The Distributive Property is used to change the form of a variable expression from factored form to
sum or difference of terms or vice versa. In general, the Distributive Property is expressed as:
a(b  c)  ab  ac and (b  c)a  ab  ac
Simplify each expression.
a) 2( x  4)
b)
3
3
10 x  
5
4
4(2 x  5)
c)
2
3

d) 5  x  y  2 
3
5

5-#1 Homework: Use separate paper. Copy each problem and show the each step in the thinking required
to get to the correct answers. Answers without supporting work will not receive credit. Work must be shown
vertically below each copied problem. Do not use a calculator. Check to see that your answer is on the list of
possible answers below the problem set. The answers are in no particular order with a few answers that you
will not use. If you can’t get a problem correct, be sure to circle it and ask about how to do it correctly
during the next class.
1. Simplify the expressions. Copy the problems onto separate paper, show all steps vertically. Work on this
paper or answers without steps will not receive any credit.
a) 10  52  20
b) 4(2)2  3(2)  8
c) 8(4  3)2
f) 60  2(2  1)3
g)
e) 2  3(4  1)
*make sure you don’t add
the 2 and 3 first
d) 4(5  2)2  8
37 7
 
5  2  10
4
h)  
5
2

3
2
i)
2 1 3
 
5 4 2
2. Substitution and Evaluation. Copy the problems onto separate paper, show all steps vertically.
a) 4 x  3, x  5
b) x  2  3 y, x  1 y  2
d) x2  y 2 , x  3 y  1
e) a 2  4a  5, a 
1
2
c) x2  3x  5, x  4
f) 5w2  3w, w  2
3. Solve each equation. Show the check. Copy the problems onto separate paper, show all steps vertically.
a) 7 x  1  3x  17
b) 3x  3  10 x  18
c) 4  3x  2   7  9 x
4. Use the distributive property to rewrite each expression without parentheses.
a) 5( x  2)
b) 3( x  4)
31
3
c)  x  
42
8
1
5 
81
2

d)  ( y  2 x)
e) 3  x  y 
f)  x  6 
2
6 
3 2
4

ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2
ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2
ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2
ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2
ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2
ANSWERS to 5-#1 HW: (in jumbled order, plus some extra answers):
7
33
4
27
1. , 8, 6, 7, 15, 17, 44, 13, 18,
2.
,
,  3, 23, 23, 25, 10, 26
5
20 225
4
3. x  5, x  5, x  4, x  3
4. 3x  12,
1
4
3
9
3
5
y  x,
x  16, x  , 5 x  10, 2  6 y  8,
x y
2
3
8
32
2
2