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1.5 “absolute value equations & inequalities”

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1.5 “absolute value equations & inequalities”. ex 1:. Solve |x| = 5. ex 1:. Solve |x| = 5. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10. ex 1:. Solve |x| = 5. - PowerPoint PPT Presentation

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Page 1: 1.5 “absolute value  equations & inequalities”
Page 2: 1.5 “absolute value  equations & inequalities”

Solve |x| = 5

Page 3: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

Page 4: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

x = 5

Page 5: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

x = 5

Page 6: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

x = 5 or x = –5

Page 7: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

|x| = a

Page 8: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| = 5

|x| = a

x = a “or” x = –a

Page 9: 1.5 “absolute value  equations & inequalities”

Solve |x| > 5

Page 10: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

Page 11: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 12: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 13: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 14: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 15: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 16: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 17: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 18: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 19: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 20: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 21: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 22: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5

Page 23: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5 or x < –5

Page 24: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5 or x < –5

Page 25: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

x > 5 or x < –5

Page 26: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

|x| > a

Page 27: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |x| > 5

|x| > a

x > a “or” x < –a

Page 28: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

Page 29: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Page 30: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Page 31: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x 5

Page 32: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x 5

Page 33: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x 5 and x –5

Page 34: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x 5 and x –5

Page 35: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x 5 and x –5

Page 36: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x –5 and x 5

Page 37: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x –5 and x 5

Page 38: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

x –5 and x 5

–5 x 5

Page 39: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

|x| < a

Page 40: 1.5 “absolute value  equations & inequalities”

Solve |x| 5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

|x| < a

x > –a “and” x < a

Page 41: 1.5 “absolute value  equations & inequalities”
Page 42: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

Page 43: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

ax + b = c or ax + b = –c

Page 44: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

ax + b = c or ax + b = –c |ax + b|

> c

Page 45: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

ax + b = c or ax + b = –c |ax + b|

> cax + b > c or ax + b < –c

Page 46: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

ax + b = c or ax + b = –c |ax + b|

> cax + b > c or ax + b < –c

|ax + b| < c

Page 47: 1.5 “absolute value  equations & inequalities”

|ax + b| = c

ax + b = c or ax + b = –c |ax + b|

> cax + b > c or ax + b < –c

|ax + b| < c

ax + b < c and ax + b > –c

Page 48: 1.5 “absolute value  equations & inequalities”

Solve |x – 4| = 2

Page 49: 1.5 “absolute value  equations & inequalities”

Solve |x – 4| = 2

x – 4 = 2 or x – 4 = –2

Page 50: 1.5 “absolute value  equations & inequalities”

Solve |x – 4| = 2

x – 4 = 2 or x – 4 = –2

x = 6 or x = 2

Page 51: 1.5 “absolute value  equations & inequalities”

Solve |6x + 3| = 15

Page 52: 1.5 “absolute value  equations & inequalities”

Solve |6x + 3| = 15

6x + 3 = 15 or 6x + 3 = –15

6x = 12 or 6x = –18 x = 2 or x = –3

Page 53: 1.5 “absolute value  equations & inequalities”

Solve |5 – 4x| + 3 = 4

Page 54: 1.5 “absolute value  equations & inequalities”

Solve |5 – 4x| + 3 = 4

|5 – 4x| = 1

Page 55: 1.5 “absolute value  equations & inequalities”

Solve |5 – 4x| + 3 = 4

|5 – 4x| = 1

5 – 4x = 1 or 5 – 4x = –1

Page 56: 1.5 “absolute value  equations & inequalities”

Solve |5 – 4x| + 3 = 4

|5 – 4x| = 1

5 – 4x = 1 or 5 – 4x = –1 –4x = –4 or –4x = –6

Page 57: 1.5 “absolute value  equations & inequalities”

Solve |5 – 4x| + 3 = 4

|5 – 4x| = 1

5 – 4x = 1 or 5 – 4x = –1 –4x = –4 or –4x = –6 x = 1 or x = 3

2

Page 58: 1.5 “absolute value  equations & inequalities”

Solve |2x + 5| 9

Page 59: 1.5 “absolute value  equations & inequalities”

Solve |2x + 5| 9

2x + 5 9 and 2x + 5 –9

Page 60: 1.5 “absolute value  equations & inequalities”

Solve |2x + 5| 9

2x + 5 9 and 2x + 5 –9 2x 4 and 2x –14

Page 61: 1.5 “absolute value  equations & inequalities”

Solve |2x + 5| 9

2x + 5 9 and 2x + 5 –9 2x 4 and 2x –14 x 2 and x –7

Page 62: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |2x + 5| 9

2x + 5 9 and 2x + 5 –9 2x 4 and 2x –14 x 2 and x –7

Page 63: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Solve |2x + 5| 9

2x + 5 9 and 2x + 5 –9 2x 4 and 2x –14 x 2 and x –7

Page 64: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

Page 65: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

Page 66: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

4x – 3 > 13 or 4x – 3 < –13

Page 67: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

4x – 3 > 13 or 4x – 3 < –13 4x > 16 or 4x < –10

Page 68: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

4x – 3 > 13 or 4x – 3 < –13 4x > 16 or 4x < –10

x > 4 or x < 52

Page 69: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

4x – 3 > 13 or 4x – 3 < –13 4x > 16 or 4x < –10x > 4 or x < 5

2–

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Page 70: 1.5 “absolute value  equations & inequalities”

Solve |4x – 3| + 7 > 20

|4x – 3| > 13

4x – 3 > 13 or 4x – 3 < –13 4x > 16 or 4x < –10x > 4 or x < 5

2–

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Page 71: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

Page 72: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

|actual weight – ideal weight| tolerance

Page 73: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

|actual weight – ideal weight| tolerance

|x – 12| 0.25

Page 74: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

|actual weight – ideal weight| tolerance

|x – 12| 0.25

x – 12 0.25 and x – 12 –0.25

Page 75: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

|actual weight – ideal weight| tolerance

|x – 12| 0.25

x – 12 0.25 and x – 12 –0.25x 12.25 and x 11.75

Page 76: 1.5 “absolute value  equations & inequalities”

A soda manufacturer has a tolerance of 0.25 ounce for a can of soda that is supposed to weigh 12 ounces. Write and solve an absolute value inequality that describes the acceptable weights for a “12 ounce” soda.

|actual weight – ideal weight| tolerance

|x – 12| 0.25

x – 12 0.25 and x – 12 –0.25x 12.25 and x 11.75

Page 77: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

1] Is x = –4 a solution to |3x + 8| = 20?

2] |5x – 4| = 16

3] |10 + 3x| – 1 17

4] Solve & graph the solution on

the # line: |4x + 11| 23

Page 78: 1.5 “absolute value  equations & inequalities”

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

1] Is x = –4 a solution to |3x + 8| = 20?

2] |5x – 4| = 16

3] |10 + 3x| – 1 17

4] Solve & graph the solution on

the # line: |4x + 11| 23

x = 4 or x =

125

NO ; 4 20

x < 3 and x >

172

x or x

283

–83