Transcript INEQUALITIES Graphing and solving INEQUALITY SYMBOLS > > = ≠ Less Than Greater Than Less Than or Equal To Greater Than or Equal To Equal To Not Equal To.

INEQUALITIES
Graphing and solving
INEQUALITY SYMBOLS
<
>
<
>
=
≠
Less Than
Greater Than
Less Than or Equal To
Greater Than or Equal To
Equal To
Not Equal To
GRAPHING SYMBOLS AND TOOLS
PEN CIRCLE – is used for <, >, and ≠. This means
the number is not included in the solution. (where
it starts)
CLOSED CIRCLE – is used for <, >, and =. This
means the number is included in the soluteon.
(where it starts)
Number Line – used for graphing
solutions to inequalities
HOW TO GRAPH
1 2
1 2
1 2
3 4
3 4
3 4
5 6 7
5 6 7
5 6 7
x>5
Where does it start?
What type of circle will be used?
Which direction will the arrow go?
x<3
Where does it start?
What type of circle will be used?
Which direction will the arrow go?
x≠4
Where does it start?
What type of circle will be used?
Which direction will the arrow go?
NOW YOU GRAPH THESE
x < 10
y>4
z=5
a≠6
b≠-8
c < -2
d > -3
RULE WHEN SOLVING INEQUALITIES
dividing or multiplying by a
negative number flip the sign.
Example: - 5x > - 25
- 5x > - 25
-5
-5
x< 5
When
SOLVING ONE STEP INEQUALITIES
c + 7 > 16
-7
c>9
-7
given
opposite of addition is subtraction
solution now we can graph it
d + -9 < 20 given
+9
+9
opposite of negative is positive
d < 29 solution now we can graph it
8r > 64
-5r > 45
s÷12 > 4
÷8
÷-5
×12
r>8
÷8
r < -9
÷-5
×12
s > 48
w÷-6 > -3
×6
×6
w < -18
YOU SOLVE AND GRAPH THESE ONE
STEP INEQUALITIES (SHOW YOUR WORK)
-56 + x > 100
x > 156
x – 10 < 20
x < 30
5p < - 30
p < -6
-7q > -49
q > -7
h ÷ -4 < -12
h < 48
m ÷ 6 > -3
m > -18
SOLVING TWO STEP INEQUALITIES
3x + 7 < 16 given
x + 6 > -6
given
-5y – (-15) < -30 given
-7
-7 opposite of addition is
3 -5y + 15 < -30 change subtraction
tosubtraction
addition
3(x + 6)
divide isofmultiply
-5y>+ (-6)
15 –315 <opposite
-30 – 15 of
opposite
is subtraction
3x < 9 addition
still not done
3 -5y < -45 not done yet
÷3 ÷3 opposite of multiply is divide
-45 ÷
-5 opposite of multiply is divide
x + 6 >-5y
-18÷ -5
still< not
done
x < 3 we have
solution
we can
y > 9 have to flip sign and now
thenow
solution
to graph
x + 6 – 6 > -18 – 6 now opposite of addition is
graph
subtraction
x > -24
now graph the solution
NOW YOU SOLVE AND GRAPH
THESE TWO STEP INEQUALITIES
x + 6 > -6
-3x + 7 ≠ -26
-10x – (-10) < 100
3
x > -24
y – (-7) < 15
-2
x ≠ 11
x < 11
y < -37