INEQUALITIES Graphing and solving. INEQUALITY SYMBOLS < > < > = ≠ Less Than Greater Than Less Than...
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Transcript of INEQUALITIES Graphing and solving. INEQUALITY SYMBOLS < > < > = ≠ Less Than Greater Than Less Than...
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