1. Inequalities
Graphing and solving

2. < > = ≠ Less Than Greater Than Less Than or Equal To
Inequality Symbols
Less Than
< > = ≠
Greater Than
Less Than or Equal To
Greater Than or Equal To
Equal To
Not Equal To

3. 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

4. How to Graph
x > 5 Where does it start? What type of circle will be used? Which direction will the arrow go? x < 3 x ≠ 4

5. Now you graph these
x < 10 y > 4 z = a ≠ b ≠ c < d > -3

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

7. Solving one step inequalities
c + 7 > 16 given opposite of addition is subtraction c > 9 solution now we can graph it d + -9 < 20 given opposite of negative is positive d < 29 solution now we can graph it 8r > 64 ÷8 ÷8 r > 8
-5r > 45
÷ ÷-5
r < -9
s÷12 > 4
× ×12
s > 48
w÷-6 > -3
×6 ×6
w < -18

8. You solve and Graph these one step inequalities (show your work)
-56 + x > 100 x – 10 < 20 5p < q > -49 h ÷ -4 < -12 m ÷ 6 > -3 x > 156 x < 30 p < -6 q > -7 h < 48 m > -18

9. Solving two step inequalities
3x + 7 < 16 given 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 > given 3
3(x + 6) > (-6) opposite of divide is multiply
x + 6 > still not done
x + 6 – 6 > -18 – 6 now opposite of addition is subtraction
x > -24 now graph the solution
-5y – (-15) < 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 divide
y > 9 have to flip sign and now we have the solution to graph

10. Now you solve and Graph these two step inequalities
x + 6 > -6 -3x + 7 ≠ x – (-10) < 100 y – (-7) < x > -24 x ≠ 11 x < 11 y < -37