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SOLUTION OF INEQUALITIES INCLUDING ABSOLUTE VALUE INEQUALITIES

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Presentation on theme: "SOLUTION OF INEQUALITIES INCLUDING ABSOLUTE VALUE INEQUALITIES"— Presentation transcript:

1 SOLUTION OF INEQUALITIES INCLUDING ABSOLUTE VALUE INEQUALITIES
Standard 1 SOLUTION OF INEQUALITIES INCLUDING ABSOLUTE VALUE INEQUALITIES END SHOW PROPERTIES OF INEQUALITY INEQUALITIES LEVEL 1 INEQUALITIES LEVEL 2 INEQUALITIES LEVEL 3 INEQUALITIES LEVEL 4 COMPOUND INEQUALITIES “OR” COMPOUND INEQUALITIES “AND” ABSOLUTE VALUE INEQUALITIES “AND” ABSOLUTE VALUE INEQUALITIES “OR” PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

2 Students solve equations and inequalities involving absolute value.
ALGEBRA II STANDARDS THIS LESSON AIMS: Standard 1: Students solve equations and inequalities involving absolute value. Estándar 6: Los estudiantes resuelven ecuaciones y desigualdades que involucran valor absoluto. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3 PROPERTIES OF INEQUALITY
Standard 1 PROPERTIES OF INEQUALITY ADDITION AND SUBTRACTION PROPERTIES OF INEQUALITY: For any numbers a, b, and c, if a>b then a+c>b+c and a-c>b-c 20 > 10 40 > 30 26 > 16 33 > 23 For any numbers a, b, and c, if a<b then a+c<b+c and a-c<b-c 12 < 22 34 < 50 17 < 27 32 < 48 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4 PROPERTIES OF INEQUALITY
Standard 1 PROPERTIES OF INEQUALITY MULTIPLICATION AND DIVISION PROPERTIES OF INEQUALITY If c>0 AND a > b then: a c b ac>bc and > 42 > 28 2 18 > 15 36 > 30 6 > 4 36 > 12 3 40 > 24 120> 72 3 > 1 If c>0 AND a < b then: a c b ac<bc and < 4 22 < 30 55 < 110 88 < 120 5 < 10 40 < 70 5 10 < 20 50< 100 4 < 7 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5 x X X F PROPERTIES OF INEQUALITY
Standard 1 PROPERTIES OF INEQUALITY MULTIPLICATION AND DIVISION PROPERTIES OF INEQUALITY If c<0 AND a > b then: a c b ac<bc and < 42 > 28 -2 18 > 15 -36 < -30 -6 < -4 25 50 X -25 -50 x 4 2 6 -2 -4 -6 8 10 -8 -10 36 > 12 -3 40 > 24 -120 < -72 -3 < -1 100 200 X -100 -200 F -2 -4 -6 -8 -10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

6 X F F X PROPERTIES OF INEQUALITY
Standard 1 PROPERTIES OF INEQUALITY MULTIPLICATION AND DIVISION PROPERTIES OF INEQUALITY If c<0 AND a < b then: a c b ac>bc and > -4 22 < 30 55 < 110 -88 > -120 -5 > -10 100 200 X -100 -200 F -2 -4 -6 -8 -10 40 < 70 -5 10 < 20 -50> -100 -4 > -7 100 200 X -100 -200 F -2 -4 -6 -8 -10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

7 x K x F x Solve these inequalities then graph the solution:
Standard 1 Solve these inequalities then graph the solution: 25 > 12 + K X + 4 < 12 X < 8 13 > K X < 8 X K <13 K < 13 K x 4 2 6 -2 -4 -6 8 10 -8 -10 5 10 15 20 25 K -5 -10 -15 -20 6X < -60 10X 20 < -9F > X 2 < F -6 < X 2 X < X < -10 F -6 F < x 4 2 6 -2 -4 -6 8 10 -8 -10 F -2 -4 -6 -8 -10 X< -10 X x 4 2 6 -2 -4 -6 8 10 -8 -10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

8 x X Z X Solve these inequalities and graph the solution: X 7 X
Standard 1 Solve these inequalities and graph the solution: 20X > -24 > 8 -16X -32 > -16X 20X > 2 < X X 7 > X > 2 X 7 X > X > 2 X x 4 2 6 -2 -4 -6 8 10 -8 -10 X 4 2 6 -2 -4 -6 8 10 -8 -10 32 < 3X- 1 10 + 4Z < 33< 3X 4Z < X>11 Z 4 < X >11 X Z 4 Z < 5 10 15 20 25 X -5 -10 -15 -20 Z 4 2 6 -2 -4 -6 8 10 -8 -10

9 Y X x R Solve these inequalities and graph the solution: + 2 < 34 X
Standard 1 Solve these inequalities and graph the solution: + 2 < 34 X 4 Y 8 > X 4 <32 (4) (4) -Y 8 36 > (-8) (-8) X < 128 X < 128 X Y < Y Y < -288 128 Y -100 -200 -300 100 200 X -100 -200 R< 2 2 3 X – 7 > +1 +1 3 2 R< 2 2 3 7 3 X 3 3 7 > R < 3 R R < 3 X 7 > X 7 X > x 4 2 6 -2 -4 -6 8 10 -8 -10 R 4 2 6 -2 -4 -6 8 10 -8 -10

10 X X Solve these inequalities and graph the solution: 12 -4X 8 8 >
Standard 1 Solve these inequalities and graph the solution: 12 -4X 8 8 > 10X - 6 4 <12 12-4X 8 8 > 10X - 6 4 <12 (8) (8) (4) (4) 64 > 12– 4X 10X – 6< 48 52 > -4X 5 10X < 54 . 2 54 10 5 4 10 = 5 2 50 -13 < X X < 5 2 4 X > -13 X > -13 X 5 2 X < X 5 10 15 20 25 X -5 -10 -15 -20 X 4 2 6 -2 -4 -6 8 10 -8 -10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

11 Standard 1 Solve this inequality and graph it: 20X +12 6X-16 + 360 > 26X – > 26X > X 14 > X 14 X > 5 10 15 20 25 X -5 -10 -15 -20 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

12 Y Y Solve these inequalities and graph them: Y Y > 15 Y Y < 4
Standard 1 Solve these inequalities and graph them: 14Y + 28 < 180 – 24Y 71 + ( Y + 4) > 90 75 + Y > 90 14Y < -24Y +152 + 24Y + 24Y Y > 15 38Y < 152 Y > 15 Y Y < 4 5 10 15 20 25 Y -5 -10 -15 -20 Y < 4 Y Y 4 2 6 -2 -4 -6 8 10 -8 -10 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13 X Solve this inequality and graph it: 2X+12 3 > 7 2X . = X X <
Standard 1 Solve this inequality and graph it: 3 7 > 2X+12 2X 6X > 7(2X+12) 6X > 14X + 84 1 -14X -14X . 4 84 8 10 4 8 = 10 1 2 -8X > 84 8 04 X< 10 1 2 - X < X 10 1 2 - 5 10 15 20 25 X -5 -10 -15 -20 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14 6+5 < X 17+X < 9 9+X 16 11 < X 9+X 16 17+X < 9 -9 -9
Standard 1 Solve these compound inequalities: 6+5 < X 17+X < 9 OR 9+X 16 > OR 11 < X 9+X 16 > 17+X < 9 X > 11 X < -8 X 7 > -8 7 x 7 x -8 x 11 5 10 15 20 25 x -5 -10 -15 -20 X | OR X<-8 X 7 > PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

15 10+2 < X 21+X < 17 11+X 15 12 < X 11+X 15 21+X < 17
Standard 1 Solve these compound inequalities: 10+2 < X 21+X < 17 OR 11+X 15 > OR 12 < X 11+X 15 > 21+X < 17 X > 12 X < -4 X 4 > -4 4 x 4 x -4 x 12 5 10 15 20 25 x -5 -10 -15 -20 X | OR X<-4 X 4 > PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

16 11+3 < X 15+X > 19 16+X 18 14 < X 16+X 18 15+X > 19
Standard 1 Solve these compound inequalities: 11+3 < X 15+X > 19 OR 16+X 18 > OR 14 < X 16+X 18 > 15+X > 19 X > 14 X > 4 X 2 > 2 x 2 x 4 x 14 5 10 15 20 25 x -5 -10 -15 -20 X | X 2 > PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

17 11+3 >X 15+X > 19 16+X 18 14 > X 16+X 18 15+X > 19 -16 -16
Standard 1 Solve these compound inequalities: 11+3 >X 15+X > 19 OR OR 16+X 18 > 14 > X 16+X 18 > 15+X > 19 X < 14 X > 4 X 2 > x 2 x 4 x 14 5 10 15 20 25 x -5 -10 -15 -20 X | R PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

18 15+8 > X 15+X > 8 8+X > 15 23 > X 8+X > 15 15+X > 8
Standard 1 Solve these compound inequalities: 15+8 > X 15+X > 8 8+X > 15 AND AND 23 > X 8+X > 15 15+X > 8 X < 23 X > -7 X > 7 x 7 x -7 x 23 5 10 15 20 25 x -5 -10 -15 -20 7 23 X | 7<X<23 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

19 (X+4)+(3X-5) > X (X+4 )+X > (3X-5) (3X-5) +X > (X+4 )
Standard 1 Solve these compound inequalities: (X+4)+(3X-5) > X (X+4 )+X > (3X-5) AND AND (3X-5) +X > (X+4 ) 4X -1 >X 2X +4 > 3X-5 4X – 5 > X +4 -4X X -2X X -X X 4 > X-5 3X – 5 > 4 -1 >-3X 3X > 9 .33 <X 9 > X X < 9 X>.33 X > 3 x 3 x 9 x .33 5 10 15 20 25 x -5 -10 -15 -20 3 9 X | 3<X< 9 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

20 6+5 < X 17+X < 9 9+X 16 11 < X 9+X 16 17+X < 9 -9 -9
Standard 1 Solve these compound inequalities: 6+5 < X 17+X < 9 AND AND 9+X 16 > 11 < X 9+X 16 > 17+X < 9 X > 11 X < -8 X 7 > x 7 x -8 x 11 5 10 15 20 25 x -5 -10 -15 -20 NO SOLUTION! PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

21 x x x X | -4<X<4 Standard 1 ABSOLUTE VALUE INEQUALITIES |X|<4
2 4 6 8 10 x -2 -4 -6 -8 X | -4<X<4 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

22 x x X X | -76<X< 64 Standard 1 SOLVE: |X + 6|< 70
X<64 X > -76 x 64 -76 64 x -76 100 200 X -100 -200 X | -76<X< 64 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

23 x x X X | -10<X< 6 Standard 1 SOLVE: |5X + 10|<40
5X > -50 5X < 30 X > -10 X < 6 x 6 -10 6 x -10 10 20 X -10 -20 X | -10<X< 6 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

24 x x X X | -5.4<X< 5 Standard 1 20|10X + 2|< 1040 SOLVE: 20
10X > -54 10X < 50 X > -5.4 X < 5 x 5 -54 5 x -5.4 5 10 X -5 -10 X | -5.4<X< 5 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

25 x x x X | X>3 Standard 1 SOLVE: |12X+20| < 16X+8
12X + 20 > -16X - 8 12X < 16X - 12 -16X X 12X > -16X - 28 -4X< - 12 +16X +16X 28X > -28 X > 3 X > -1 3 x -1 x 3 2 4 6 8 10 x -2 -4 -6 -8 X | X>3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

26 x x x X | OR X<-6 X>6 Standard 1 ABSOLUTE VALUE INEQUALITIES
2 4 6 8 10 x -2 -4 -6 -8 X | OR X<-6 X>6 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

27 x x X X | OR X<-55 X>45 Standard 1 SOLVE: |X + 5|> 50
X > 45 X < -55 x 45 -55 45 x -55 100 200 X -100 -200 X | OR X<-55 X>45 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

28 x x X X | OR X<-10 X>6 Standard 1 SOLVE: |15X + 30|>120
15X < -150 15X > 90 X < -10 X > 6 x 6 -10 6 x -10 20 40 X -20 -40 X | OR X<-10 X>6 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

29 Standard 1 |5X -1|> -3 |2X + 7 | + 76 < 20 |2X + 7 | < -56
SPECIAL CASES TO PAY ATTENTION! SOLVE: |5X -1|> -3 Solution are all reals because absolute value is always positive and greater than any negative value. SOLVE: |2X + 7 | + 76 < 20 |2X + 7 | < -56 No solution because absolute value is always positive and never less than a negative value. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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