Download Graphing Inequalities and Equation Solutions

Graphing Inequalities
and Equation Solutions
OCTOBER 3, 2016
Outline
Graphing directions
Graphing Less than and Greater than Inequalities
Graphing Less than or Equal to and Greater than or Equal to
Inequalities
Examples
Solution Types for Equations
Examples
Graphing Instructions
1. Draw a number line that includes numbers before and after
solution.
2. If the symbol is < or >, then put an open circle over the
number in the solution. If the symbol is ≤ 𝑜𝑟 ≥ then put a
closed circle over the number in the solution.
3. Draw an arrow in the direction of symbol (i.e. if the symbol is
< then draw an arrow pointing ←)
Graphing Less than and Greater than
Inequalities
Less Than (<)
◦ x<9
-1 0 1 2 3
Less Than (<)
◦ x < -5
-6 -5
-2 -1 0
9
Graphing Less than and Greater than
Inequalities
Greater Than (>)
◦ x > -6
-6 -5
-1 0 1 2 3
Greater Than (>)
◦ x>7
0 1 2
7
8
Graphing Less than or Equal to
Inequalities
Less Than or Equal to (≤)
◦ x ≤ 10
-1 0 1 2 3
Less Than or Equal to (≤)
◦ x ≤ -6
-6 -5
-2 -1 0
10
Graphing Greater than or Equal to
Inequalities
Greater Than or Equal to (≥)
◦ x ≥ -5
-6 -5
-1 0 1 2 3
Greater Than or Equal to (≥)
◦ x≥8
0 1 2
7
8
Example
Step 1: x +20 < 39
Step 2: x +20 - 20 < 39 - 20
Step 3: x +(20 -20) < (39 -20)
x + (0) < (19)
x < 19 (All numbers less than 19)
0 1
19
Example
Step 1: x -12 > 25
Step 2: x -12 +12 > 25 +12
Step 3: x +(-12 +12) > (25 +12)
x + (0) > (37)
x > 37 (All numbers greater than 37)
37 38
Example
Step 1: d - 8 ≥ 24
Step 2: d -8 + 8 ≥ 24 + 8
Step 3: d +(-8 + 8) ≥ (24 +8)
d + (0) ≥ (32)
d ≥ 32 (All numbers greater than or equal to 32)
0 1
31 32
Example
Step 1: 17y ≤ 68
17𝑦
)
17
17𝑦
3: ( )
17
Step 2: (
Step
68
17
68
( )
17
≤( )
≤
y(1) ≤ (4)
y ≤ 4 (All numbers less than or equal to 4)
3 4
Equation Solutions
Infinite Solutions
◦Occurs when both sides of an equation equal zero
◦Example
◦ 2y+6=2y+6
◦ 2y+6-6=2y+6-6
◦ 2y+0=2y+0
◦ 2y=2y
◦ 2y-2y=2y-2y
◦ 0=0 (True)
Equation Solutions
No Solutions
◦Occurs when one side of an equation equals zero and the other
side is a non-zero integer
◦Example
◦ 4d+8=4d+6
◦ 4d+8-8=4d+6-8
◦ 4d+0=4d-2
◦ 4d=4d-2
◦ 4d-4d=4d-4d-2
◦ 0=-2 (False)
Solving for Variable
Problem 1: Solve the following equation for L
A=LW
𝐴 𝐿𝑊
1.
=
2.
3.
𝑊 𝑊
𝐴
=L
𝑊
𝐴
L=
𝑊
Problem 2: Solve the following equation for A
B=A+C
1. B-C=A+C-C
2. B-C=A
3. A=B-C
Example
◦ 4g-12=4(g-3)
◦ 4g-12=4g-12
◦ 4g-12+12=4g-12+12
◦ 4g+0=4g+0
◦ 4g=4g
◦ 4g-4g=4g-4g
◦ 0=0
◦ Infinite Solutions
Example
◦ 7h-13=7h+13
◦ 7h-13+13=7h+13+13
◦ 7h+0=7h+26
◦ 7h=7h+26
◦ 7h-7h=7h-7h+26
◦ 0=26
◦ No Solutions