INEQUALITIES Graphing and solving INEQUALITY SYMBOLS Less Than

INEQUALITIES Graphing and solving

INEQUALITY SYMBOLS < > = ≠ Less Than Greater Than Less Than or Equal To Greater Than or 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 3 4 3 4 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: - 5 x > - 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 8 r > 64 -5 r > 45 s÷ 12 > 4 ÷ 8 ÷-5 × 12 r>8 ÷ 8 r < -9 ÷-5 × 12 s > 48 w÷-6 > -3 × 6 w < -18

-56 + x > 100 x > 156 YOU SOLVE AND GRAPH THESE ONE STEP INEQUALITIES (SHOW YOUR WORK) x – 10 < 20 x < 30 5 p < - 30 p < -6 -7 q > -49 q > -7 h ÷ -4 < -12 h < 48 m ÷ 6 > -3 m > -18

SOLVING TWO STEP INEQUALITIES 3 x + 7 < 16 given x + 6 > -6 given -5 y – (-15) < -30 given -7 -7 opposite of addition is 3 -5 y + 15 < -30 change subtraction to addition subtraction 3(x + 6) ofopposite divide is of multiply -5 y>+ (-6) 15 – 3 15 opposite < -30 – 15 subtraction 3 x < 9 addition still notisdone 3 -5 y < -45 not done yet ÷ 3 opposite of multiply is divide < -45 ÷ -5 opposite of multiply is divide x + 6 >-5 y -18÷ -5 still not done x <we 3 have solution now we graph y > 9 have to flip sign and now the solution to can graph x + 6 – 6 > -18 – 6 now opposite of addition is subtraction x > -24 now graph the solution

NOW YOU SOLVE AND GRAPH THESE TWO STEP INEQUALITIES x + 6 > -6 -3 x + 7 ≠ -26 -10 x – (-10) < 100 3 x > -24 y – (-7) < 15 -2 x ≠ 11 x < 11 y < -37