Transcript Multiply same base

Absolute
Value
4
4  6
Make it
positive
4 4
4  6  4  6  2
Properties:
Commutative
Associative
Identity
Properties
• Commutative – change order
x 3  3 x
• Associative – change parentheses
 x  3  2  x  (3  2)
• Identity – stays the same
3(1)  3 or
x0  x
Combine Like
Terms
3x  7 y  x  2 y
2
2
Add (or subtract) the
coefficients of like
terms
3x  7 y  x  2 y  2 x  9 y
2
2
2
Distribution
3  x  7 
  x  3
Multiply by every
term in the
parentheses
3  x  7   3x  21
  x  3  1( x  3)  1x  3
Graphing
Inequalities
x5
x5
x5
x5
Graphing
Inequalities on a
number line
x5
x5
x5
x5
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
Graphing Linear Inequalities
• Dashed or solid line
• Shade above or below
Graphing Linear Inequalities
Words to algebra
expression
• Product of 3 and a number
• Quotient of 3 and a number
• Sum of 3 and a number
• 3 less than a number
• Four times a sum of 3 and a number
• Product of 3 and a number 3x
• Quotient of 3 and a number 3
x
• Sum of 3 and a number 3  x
• 3 less than a number
x 3
• Four times a sum of 3 and a
number 4(3  x)
Reciprocal
3
4
Reciprocal – flip top
to bottom, bottom to
top
Reciprocal of
3
is
4
4
3
Steps to solve
equations
Steps to solve
equations
•
•
•
•
Distribute to remove parentheses
Combine like terms on same side of =
Move variable to left by adding opposite
Move number to right by adding
opposite
• Divide by coefficient of variable
Solving Inequalities
What do I remember to do when I
divide or multiply by a negative
number?
Example: -2x < 8
Solving Inequalities
What do I remember to do when I
divide or multiply by a negative
number? SWITCH THE SIGN!
Example: -2x < 8
2 x 8

2 2
x  4
Solving Inequalities
What do I do when I solve and the
variable ends up on the right?
Example: 8 < x
Solving Inequalities
• What do I do when I solve and the
variable ends up on the right?
• Switch the order, switch the
sign.
• Example: 8 < x changes to:
x>8
Solving Inequalities
How do I solve a 3-part inequality?
Example: 4< 2x+1 < 8
Solving Inequalities
How do I solve a 3-part inequality?
Get x alone in the middle, between 2
numbers. Do the same operation left,
center, and right.
Example: 4< 2x+1 < 8
-1
-1 -1
3 < 2x < 7
3/2 < x < 7/2
Notes about
Functions
• Domain is…
• Range is…
• f(x) means…
• It’s a function if…
Notes about
Functions
• Domain is… all the x values
• Range is… all the y values
• f(x) means… plug in x to get y
• It’s a function if… no x’s are repeated
or no points are in a vertical line.
Correlation on Scatter Plots
• How do I draw the
trend line?
• Direction of negative
correlation
• Direction of positive
correlation
y
6
5
4
3
2
1
1
2
3
4
5
6
x
y
6
5
4
3
2
1
1
2
3
4
5
6
x
Correlation on Scatter Plots
• How do I draw the
trend line? Straight
through the middle
• Direction of negative
correlation: down to
the right
• Direction of positive
correlation: up to the
right
y
6
5
4
pos
3
2
1
1
2
3
4
5
6
x
y
6
5
neg
4
3
2
1
1
2
3
4
5
6
x