INEQUALITIESGraphing and solving

INEQUALITY SYMBOLS

< > < > = ≠

Less Than

Greater Than

Less Than or Equal To

Greater Than or Equal ToEqual ToNot 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 GRAPHx > 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?

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

NOW YOU GRAPH THESEx < 10 y > 4 z = 5 a ≠ 6 b ≠ - 8 c < -2 d > -3

RULE WHEN SOLVING INEQUALITIES

When dividing or multiplying by a negative number flip the sign.Example: - 5x > - 25 - 5x > - 25 - 5 - 5 x < 5

SOLVING ONE STEP INEQUALITIES

c + 7 > 16 given

- 7 -7 opposite of addition is subtraction

c > 9 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

÷8 ÷8

r > 8

-5r > 45

÷-5 ÷-5

r < -9

s÷12 > 4

×12 ×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 – 10 < 20 5p < - 30 -7q > -49 h ÷ -4 < -12 m ÷ 6 > -3

x > 156 x < 30 p < -6 q > -7 h < 48 m > -18

SOLVING TWO STEP INEQUALITIES3x + 7 < 16 given

-7 -7 opposite of addition is subtraction

3x < 9 still not done ÷3 ÷3 opposite of multiply is divide x < 3 solution now we can graph

x + 6 > -6 given 33(x + 6) > (-6) 3 opposite of divide is multiply 3x + 6 > -18 still not done x + 6 – 6 > -18 – 6 now opposite of addition is

subtraction x > -24 now graph the solution

-5y – (-15) < -30 given-5y + 15 < -30 change subtraction to addition -5y + 15 – 15 < -30 – 15 opposite of addition is subtraction-5y < -45 not done yet-5y ÷ -5 < -45 ÷ -5 opposite of multiply is dividey > 9 have to flip sign and now we have the solution to graph

NOW YOU SOLVE AND GRAPH THESE TWO STEP INEQUALITIES

x + 6 > -6 -3x + 7 ≠ -26 -10x – (-10) < 100 y – (-7) < 15

3 -2

x > -24 x ≠ 11 x < 11 y < -37