1.6

1
1.6 Solving Compound and Absolute Value
Inequalities
2
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.

3
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17

4
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17

5
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7

6
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7

7
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7

8
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17

9
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17

10
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7

11
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6

12
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt

13
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt 2x

14
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt 2x
• 2 2

15
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt 2x
• 2 2
• 3

16
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt 2x
• 2 2
• 3 lt

17
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7
• 6 lt 2x
• 2 2
• 3 lt x

18
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x
• 2 2
• 3 lt x

19
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x
• 2 2
• 3 lt x

20
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x lt
• 2 2
• 3 lt x

21
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x lt 10
• 2 2
• 3 lt x

22
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x

23
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x

24
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x lt

25
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x lt 5

26
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x lt 5

27
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x lt 5
• 3 lt x

28
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x

29
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x lt 5

30
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

31
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

0
3
5
32
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

0
3
5
33
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

0
3
5
34
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

0
3
5
35
1.6 Solving Compound and Absolute Value
Inequalities

• Example 1 Solve 13 lt 2x 7 17 and graph the
  solution on a number line.
• 13 lt 2x 7 17
• 13 lt 2x 7 2x 7 17
• -7 -7 -7 -7
• 6 lt 2x 2x 10
• 2 2 2 2
• 3 lt x x 5
• 3 lt x 5

0
3
5
36

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.

37

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.

38

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3

39

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3

40

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4

41

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

42

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

43

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
44

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
45

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
46

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
47

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
48

• Example 2 Solve y 2 gt -3 or y 4 -3 and
  graph the solution on a number line.
• y 2 gt -3 or y 4 -3
• y 2 gt -3 or y 4 -3
• 2 2 -4 -4
• y gt -1 or y -7

-7
-1
0
49

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.

50

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4

51

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4

52

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4

-4
0
4
53

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4
• (b) Solve a gt 4. Graph the solution on a
  number line.

-4
0
4
54

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4
• (b) Solve a gt 4. Graph the solution on a
  number line.
• a gt 4

-4
0
4
55

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4
• (b) Solve a gt 4. Graph the solution on a
  number line.
• a gt 4
• a gt 4 or a lt -4

-4
0
4
56

• Example 3
• (a) Solve a lt 4. Graph the solution on a
  number line.
• a lt 4
• a lt 4 or a gt -4
• (b) Solve a gt 4. Graph the solution on a
  number line.
• a gt 4
• a gt 4 or a lt -4

-4
0
4
-4
0
4
57

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.

58

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6

59

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6

60

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6

61

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6
• 12 12 _ 12 12

62

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6
• 12 12 _ 12 12
• 3x 18 3x lt 6

63

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6
• 12 12 _ 12 12
• 3x 18 3x lt 6
• 3 3 3
  3

64

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6
• 12 12 _ 12 12
• 3x 18 3x lt 6
• 3 3 3
  3
• x 6 x lt 2

65

• Example 4 Solve 3x 12 6 and graph the
  solution on a number line.
• 3x 12 6
• 3x 12 6 3x 12 lt -6
• 12 12 _ 12 12
• 3x 18 3x lt 6
• 3 3 3
  3
• x 6 x lt 2

0
2
6