Winky & Squinty Face
Which is squinty face and which is winky face?
5 + (-1)
10 - (-9)
5 + (-1) --> winky face
10 - (-9) --> squinty face
What operation is it when a number is touching parentheses?
Example: 6(10)
Multiplication
6(10) is the same as 6 • 10
Addition
What is the opposite operation of multiplication?
What is the opposite operation of addition?
Division
Subtraction
Which inequality signs would be graphed with closed circles?
Which inequality signs would be graphed with open circles?
closed circles: ≤, ≥
open circles: <, >
Simplify but don't solve:
6 + (-2)
6 - 2
A winky face +(- becomes subtract
A minus in front of a number can usually count as a _________.
If there is no number in front of parentheses, then there is always an invisible ____.
Multiplying two negative numbers creates a ______ number.
1) negative
2) one
3) positive
Combine & simplify:
2x + 9 + 5x + 1
7x + 10
2x + 5x = 7x, 9 + 1 = 10
Solve:
x - 10 = 2
x = 12
(add 10 to both sides)
x ≤ -2
closed circle, arrow to the left, starting at -2
Simplify but don't solve:
-8 - (-10)
-8 + 10
A squinty face -(- becomes addition
Distribute:
5(x + 2)
5x + 10
5 • x = 5x, 5 • 2 = 10 --> 5x + 10
Combine & Simplify:
(3x + 4) + (8x - 20)
11x - 16
(3x + 4) + (8x - 20) --> 3x + 4 + 8x - 20
3x + 8x = 11x, 4 + -20 = -16 --> 11x - 16
Solve:
0.5x + 12 = 3
x = -18
(subtract 12 from both sides)
(then divide by 0.5 on both sides)
Graph:
14 > x
open circle, arrow going to the left, starting at 14
Simplify & Solve
-10 - (-13)
-10 + 13
= 3
(Squinty face becomes addition)
Distribute:
-2(3x + 14)
-6x - 28
-2 • 3x = -6x, -2 • 14 = -28 --> -6x - 28
(-12x + 2) - (10x + 4)
-22x - 2
(-12x + 2) - (10x + 4) --> -12x + 2 - 10x - 4
-12x + -10x = -22x, 2 + -4 = -2 --> -22x - 2
20 = x/3 + 4
x = 48
(subtract 4 from both sides)
(then multiply by 3 on both sides)
Solve and graph:
14x + 1 > -27
x > -2 & open circle, arrow towards the right
(subtract 1 from both sides)
(then divide by 14 on both sides)
(there is no flip because you divide by a positive, not a negative)
Simplify & Solve
3 + (-8) - (-12) + (-1)
3 - 8 + 12 - 1
= 6
Distribute:
-4(2x - 8)
-8x + 32
-4 • 2x = -8x, -4 • -8 = 32 --> -8x + 32
6(x - 12) + 2(10x - 4)
26x - 80
6(x - 12) + 2(10x - 4) --> 6x - 72 + 20x - 8
6x + 20x = 26x, -72 + -8 = -80 --> 26x - 80
4(x - 10) = 20
x = 15
(distribute: 4x - 40 = 20)
(add 40 to both sides)
(then divide by 4 on both sides)
Solve & Graph:
18 ≤ -3x
-6 ≥ x or x ≤ -6
Graph: closed circle, arrow towards the left
(divide by -3 on both sides)
(that flips the sign because you divide by a negative)