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Inequalities Graphing and solving

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**< > = ≠ 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

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**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

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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

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

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**Rule when solving inequalities**

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

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**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

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**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

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**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

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**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

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