Inequalities Day 5
Before today I can graph, solve, and write multi-step
inequalities.
After today I can solve, graph, and write compound
inequalities
a) Do Now: Find new Seats! Then grab a homework key and
review your homework. Ask questions when you finish.
b) Begin Block 6
c) Lesson 3.5- have out notes!
d) Work time- What questions do you have?!
HomeworkBlock 6
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
(For help, go to Lessons 1-1 and 3-1.)
Graph each pair of inequalities on one number line.
<
<
>
>
1. c < 8; c 10
2. t –2; t –5
3. m 7; m > 12
Use the given value of the variable to evaluate each expression.
4. 3n – 6; 4
6. 12 + 13 + y ; 17
3
5. 7 – 2b; 5
7. 2d – 3 ; 9
5
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solutions
1. c < 8; c >10
2. t > –2; t <–5
3. m < 7; m > 12
4. 3n – 6 for n = 4: 3(4) – 6 = 12 – 6 = 6
5. 7 – 2b for b = 5: 7 – 2(5) = 7 – 10 = –3
6. 12 + 13 + y for y = 17: 12 + 13 + 17 = 42 = 14
3
7. 2d – 3
5
3
3
for d = 9: 2(9) – 3 = 18 – 3 = 15 = 3
5
5
5
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write two compound inequalities that represent each situation.
Graph the solutions.
a. all real numbers that are at
least –1 and at most 3.
b. all real numbers that are at less
than 31, but greater than 25.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write two compound inequalities that represent each situation.
Graph the solutions.
a. all real numbers that are at
least –1 and at most 3.
b > –1 and b < 3
b. all real numbers that are at less
than 31, but greater than 25.
–1 < b < 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write two compound inequalities that represent each situation.
Graph the solutions.
a. all real numbers that are at
least –1 and at most 3.
b > –1 and b < 3
b. all real numbers that are at less
than 31, but greater than 25.
–1 < b < 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write two compound inequalities that represent each situation.
Graph the solutions.
a. all real numbers that are at
least –1 and at most 3.
b > –1 and b < 3
b. all real numbers that are at less
than 31, but greater than 25.
31 > n and n > 25
–1 < b < 3
3-5
Wednesday, November 20, 13
31 > n > 25
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write two compound inequalities that represent each situation.
Graph the solutions.
a. all real numbers that are at
least –1 and at most 3.
b > –1 and b < 3
b. all real numbers that are at less
than 31, but greater than 25.
31 > n and n > 25
–1 < b < 3
3-5
Wednesday, November 20, 13
31 > n > 25
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
3-5
Wednesday, November 20, 13
5–f>2
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
5–5>5–f–5
0 > –f
0
–f
<
–1
–1
3-5
Wednesday, November 20, 13
5–f>2
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
5–5>5–f–5
5–f–5>2–5
0 > –f
–f > –3
0
–f
<
–1
–1
–f
–3
<
–1
–1
3-5
Wednesday, November 20, 13
5–f>2
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
5–5>5–f–5
5–f–5>2–5
0 > –f
–f > –3
0
–f
<
–1
–1
–f
–3
<
–1
–1
3-5
Wednesday, November 20, 13
5–f>2
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
5–5>5–f–5
5–f–5>2–5
0 > –f
–f > –3
0
–f
<
–1
–1
0<f
–f
–3
<
–1
–1
and
0<f<3
3-5
Wednesday, November 20, 13
5–f>2
f<3
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve 5 > 5 – f > 2. Graph the solutions.
Write the compound inequality as two inequalities joined by and .
5>5–f
and
5–5>5–f–5
5–f–5>2–5
0 > –f
–f > –3
0
–f
<
–1
–1
0<f
–f
–3
<
–1
–1
and
0<f<3
3-5
Wednesday, November 20, 13
5–f>2
f<3
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Your test grades in science so far are 83 and 87. What possible
grades g can you make on your next test to have an average between 85
and 90?
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Your test grades in science so far are 83 and 87. What possible
grades g can you make on your next test to have an average between 85
and 90?
Relate:
Write:
85
85
is less than
or equal to
<
the average
83 + 87 + gg
3
3-5
Wednesday, November 20, 13
which is less
than or equal to
90
<
90
Compound Inequalities
ALGEBRA 1 LESSON 3-5
(continued)
85
<
83 + 87 + g
3
< 90
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
(continued)
85
3(85)
255
83 + 87 + g
3
<
< 3
<
(
< 90
)
83 + 87 + g
3
< 3(90)
Multiply by 3.
170 + g
< 270
Simplify.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
(continued)
85
3(85)
83 + 87 + g
3
<
< 3
(
< 90
)
83 + 87 + g
3
< 3(90)
Multiply by 3.
< 270
Simplify.
< 270 – 170
Subtract 170.
< 100
Simplify.
255
<
170 + g
255 – 170
<
170 + g – 170
85
<
g
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
(continued)
85
3(85)
83 + 87 + g
3
<
< 3
(
< 90
)
83 + 87 + g
3
< 3(90)
Multiply by 3.
< 270
Simplify.
< 270 – 170
Subtract 170.
< 100
Simplify.
255
<
170 + g
255 – 170
<
170 + g – 170
85
<
g
The third test grade must be between 85 and 100, inclusive.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write an inequality that represents each situation.
Graph the solutions.
a. all real numbers that are
less than 0 or greater than
3.
b. Discounted tickets are available to
children under 7 years old or to
adults 65 and older.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write an inequality that represents each situation.
Graph the solutions.
a. all real numbers that are
less than 0 or greater than
3.
b. Discounted tickets are available to
children under 7 years old or to
adults 65 and older.
n < 0 or n > 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write an inequality that represents each situation.
Graph the solutions.
a. all real numbers that are
less than 0 or greater than
3.
b. Discounted tickets are available to
children under 7 years old or to
adults 65 and older.
n < 0 or n > 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write an inequality that represents each situation.
Graph the solutions.
a. all real numbers that are
less than 0 or greater than
3.
b. Discounted tickets are available to
children under 7 years old or to
adults 65 and older.
a < 7 or a >65; because
age cannot be negative, a
> 0.
n < 0 or n > 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Write an inequality that represents each situation.
Graph the solutions.
a. all real numbers that are
less than 0 or greater than
3.
b. Discounted tickets are available to
children under 7 years old or to
adults 65 and older.
a < 7 or a >65; because
age cannot be negative, a
> 0.
n < 0 or n > 3
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3x + 2 < –7
or
3-5
Wednesday, November 20, 13
–4x + 5 < 1
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3x + 2 < –7
or
3x + 2 – 2 < –7 – 2
3x < –9
3x
–9
<
3
3
3-5
Wednesday, November 20, 13
–4x + 5 < 1
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3x + 2 < –7
or
3x + 2 – 2 < –7 – 2
–4x + 5 – 5 < 1 – 5
3x < –9
–4x < –4
3x
–9
<
3
3
–4x
–4
> –4
–4
3-5
Wednesday, November 20, 13
–4x + 5 < 1
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3x + 2 < –7
or
3x + 2 – 2 < –7 – 2
–4x + 5 – 5 < 1 – 5
3x < –9
–4x < –4
3x
–9
<
3
3
–4x
–4
> –4
–4
x < –3
or
3-5
Wednesday, November 20, 13
–4x + 5 < 1
x>1
Compound Inequalities
ALGEBRA 1 LESSON 3-5
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph
the solution.
3x + 2 < –7
or
3x + 2 – 2 < –7 – 2
–4x + 5 – 5 < 1 – 5
3x < –9
–4x < –4
3x
–9
<
3
3
–4x
–4
> –4
–4
x < –3
or
3-5
Wednesday, November 20, 13
–4x + 5 < 1
x>1
WHAT QUESTIONS
DO YOU HAVE!?!
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
pages 163–166 Exercises
11. 5 < x < 8;
1. –4 < x and x < 6
12. –2 < m
or –4 < x < 6;
2. 2 n and n 9
<
<
–
or 2 n 9; –
<
–c < 23.5;
–
3. 23 < <
13. 3
1;
<
–
s < 4;
15. 1
1
2; 2
4. 40
w
<
–t<3 ;
14. 1 <
r
–< r<
– 1.5;
16. –2<
74;
a <
–17;
5. –5 <
– j <<
–5;
17. 5
6. 1
18. 1 <– x <<
–7;
19. –1 x 11;
w
5;
7. 2 <
< n 6;
– <
–
8. –4 < p< –2;
–
9. 1 < x < 3;
<
–
10. –1.5 < w 3.5;
20. n <–3 or
n 5,
<
– –
21. x < 3 or x > 7;
<
>
–
–
22. h < 1 or h > 3;
<
–
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
23. b < 100 or b > 300;
34. –2 < x < 3
24. b < –2 or b > 2;
35. x < –3 or x >
–2
25. k < –5 or k > –1;
36. x ≤ 0 or x > 2
26. c < 2 or c >
– 3;
37. –4 <
– x <
–3
38. q ≤ –2 2 or q > 4
27. a
4 or a > 5;
3
<
28. c – 2 or c >
– 3;
– –2 or y > 5;
29. y <
–
30. d <
– –3 or d >
– 0;
31. z <<
– 2; A
– –1 or z >
39. h < –7 or h > 4
40. 4 ≤ t ≤14
41. r < 16 or r > 25
42. –6 ≤ t < 1
32. x < –3 or x > 5;
43. x < –6 or x > 9
33. n < –5 or n > 3;
44. 20 ≤ d ≤ 32
45. all real numbers except 5
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
46. The word “and” means
both statements must
be true. The word “or”
means that at least one
of the statements must
be true.
47. 2.5 < x < 7.5
48. 6 < x < 30
49. 7 < x < 49
50. 11 < x < 21
51. 66 <
– C<
– 88
52. 15 <
– D<
– 30
53. Charlotte: 29 < C <
90
–
–
Detroit: 15 <
– D<
– 83
54. Answers may vary. Sample:
Elevation near a coastline
varies between 2 m below
and 8 m above sea level.
55.
56. –2 < x < 0 or 0 < x < 3
57. n = 0 or n >
–3
58. a. 130 <
–R <
– 157
b. 20 years old
59. 16, 18, 20
60. 10, 12, 14
61. B
62. G
3-5
Wednesday, November 20, 13
Compound Inequalities
ALGEBRA 1 LESSON 3-5
63. [2] 35 <
–10.4 + 0.0059g <
– 50
24.6 <
– 0.0059g <
– 39.6
4169 < g < 6712
minimum consumption: 4169 gal
maximum consumption: 6712 gal
(OR equivalent explanation)
[1] incorrect answer OR insufficient explanation
64. b > 1
3
65. n <
– 3
66. r <
–7
67. x = –1
68. w = 2
69. identity
3-5
Wednesday, November 20, 13
Wednesday, November 20, 13