Name: _____________________________________
Period: _____________
Chapter #3: Inequalities
Date: ______________
Homework Packet #6
Days 1 – 5
COMPLETE THE FOLLOWING IN PENCIL ONLY. After completing the assignment, use the answer key
and a COLORED PEN to correct your work. Use your notes to help you answer the following. Answers are
provided.
#1 Intro to Inequalities
Graph each inequality and write in interval notation.
1. 𝑛 < 2
2. 𝑎 ≥ 0
4. −3 ≥ 𝑥
5.
ℎ<
3. −6 < 𝑛
2
6.
3
−1
2
≥𝑚
Write the inequality that matches each graph below. Then write your answer in interval and set builder
notation.
7.
8.
9.
Write the
Inequality
Set Builder
Notation
Interval
Notation
1
MIXED REVIEW:
Solve each absolute value equation below.
10. |2x – 5| = 7
11. |4x – 3| = 17
𝑥
12. |3 − 8| = 12
State the coordinates of each point from the given graph.
13. a: (____,____)
14. b: (____,____)
15. c: (____,____)
16. d: (____,____)
17. e: (____,____)
2
#2 Solving One-Step Inequalities
1.
−12 > 𝑥 − 7
2.
4.
32 ≥ −16𝑝
5.
1
9
3.
1
6.
𝑐+4 > 4
𝑛 − 6 ≤ −14
Solve
Graph
Interval
Notation
Set
Notation
−5
6
𝑦 > 12
5𝑑 ≥ −105
Solve
Graph
Interval
Notation
Set
Notation
3
7.
ERROR ANALYSIS: Taro and Jamie are solving 6𝑑 ≥ −84. Their work is shown below. Who is correct?
Explain your reasoning by describing the mistake.
MIXED REVIEW:
For #8-9, write an inequality that describes the real-world situations below. Be sure to define your variable.
8. The restaurant can seat, at most, 172 people.
9. A person has to be at least 21 years of age to drink
an alcoholic beverage.
Graph each inequality and write the interval notation.
10.
t < -4
11.
8≥𝑏
12. Is -4 a solution to 6x > -24?
4
#3 Multi-Step Inequalities
1. Determine whether each number is a solution of 4𝑥 + 8 ≥ 20. Show all work to justify your answer.
a) 3
b) -3
2. Determine whether each number is a solution of 3𝑥 − 2 < 4. Show all work to justify your answer.
a) -1
b) 2
Solve and graph each inequality. Write your answer in interval and set notation.
3.
−3𝑥 + 6 < 27
4.
1
2
𝑥 − 5 ≤ −7
graph:
graph:
interval:
interval:
set-builder:
set-builder:
5
Solve and graph each inequality. Write your answer in interval and set notation.
5.
6𝑥 + 2 − 8𝑥 < 14
6.
8𝑥 ≥ 5(2𝑥 + 4)
7.
7𝑥 − 4 ≤ 6 + 2𝑥
8.
3(𝑥 − 4) + 2 ≥ 𝑥 + 12
6
#4 Writing Compound Inequalities
Graph each compound inequality. Write the interval and set builder notation.
1.
𝑥 < 3 𝑎𝑛𝑑 𝑥 > −3
2.
𝑥 < −2 𝑜𝑟 𝑥 > 4
3.
𝑥 ≥ −2 𝑎𝑛𝑑 𝑥 ≤ 7
Interval:
Interval:
Interval:
Set Builder:
Set Builder:
Set Builder:
4.
𝑥 ≤ 0 𝑎𝑛𝑑 𝑥 > −5
5.
𝑥 ≥ 5 𝑜𝑟 𝑥 ≤ −4
6.
𝑥 < −6 𝑜𝑟 𝑥 ≥ 6
Interval:
Interval:
Interval:
Set Builder:
Set Builder:
Set Builder:
7
Given the graph of a compound inequality, write the compound inequality, interval notation, and set builder
notation.
7.
8.
9.
Compound Inequality:
Compound Inequality:
Compound Inequality:
Interval:
Interval:
Interval:
Set Builder:
Set Builder:
Set Builder:
MIXED REVIEW:
Solve and graph each inequality. Write your answer in interval and set notation.
10.
3(7𝑛) < 6𝑛 + 30
12.
3(4𝑚 + 6) ≤ 42 + 3(2𝑚 − 4)
11.
7 + 𝑦 ≤ 2(𝑦 + 3) + 2
8
#5 Solving Compound Inequalities
For #1-3, solve, graph, and write the solution set in set builder notation.
1.
2𝑦 + 4 > 0 𝑎𝑛𝑑 𝑦 ≤ 1
3.
7𝑣 − 5 ≥ 65 𝑜𝑟 − 3𝑣 − 2 ≥ −2
2.
−7 ≤ 𝑥 − 5 ≤ 0
For #4-6, solve, graph, and write the solution set in interval notation.
4.
−50 < 7𝑘 + 6 < −8
5.
−1 + 5𝑛 > −26 𝑎𝑛𝑑 7𝑛 − 2 ≤ 12
9
6.
2𝑛 + 7 ≥ 27 𝑜𝑟 3 + 3𝑛 ≤ 30
MIXED REVIEW:
For #7-8, translate each sentence into a mathematical equation.
7. Three times r subtracted from 15 is 6.
____________________
8. The sum of 8 and three times k is the same as 14.
____________________
9. A hiker walked 12.8 miles in three hours. He walked an additional 17.2 miles in 5 hours. What is his average speed
for the entire walk, in miles per hour?
10. The greater of 2 numbers is 1 more than twice the smaller. Three times the greater exceeds 5 times the smaller by 10.
Find the numbers.
10
HW PACKET #6 ANSWERS:
#1 Intro to Inequalities
#2 Solving One-Step Inequalities
1. (−∞, 2)
Graph:
[0,
2.
∞)
Graph:
3. (−6, ∞)
Graph:
4. (−∞, −3]
Graph:
1. 𝑥 < −5, (− ∞, −5), {𝑥|𝑥 < −5}
Graph:
{𝑐|𝑐
(2,
2. 𝑐 > 2,
∞),
> 2}
Graph:
3. 𝑛 ≤ −8, (−∞, −8], {𝑛|𝑛 ≤ −8}
Graph:
4. 𝑝 ≥ −2, [−2, ∞), {𝑝|𝑝 ≥ −2}
Graph:
2
3
1
5. (−∞, )
Graph:
6.
1
(−∞, −
2
]
Graph:
7. 𝑥 ≥ −3, {𝑥|𝑥 ≥ −3}, [−3, ∞)
8. 𝑥 < 2, {𝑥|𝑥 < 2}, (−∞, 2)
9. 𝑥 > −2.5, {𝑥|𝑥 > −2.5}, (−2.5, ∞)
Mixed Review:
10. {−1, 6}
7
2
11. {− , 5}
12.
13.
14.
15.
16.
17.
{-12, 60}
(-6, 4)
(7, 6)
(-8, -2)
(4, -7)
(5, 0)
1
1
5. 𝑦 < − 10 , (−∞, − 10), {𝑦|𝑦 < − 10}
Graph:
6. 𝑑 ≥ −21, [−21, ∞), {𝑑|𝑑 ≥ −21}
Graph:
7. Taro, provide an explanation
Mixed Review:
8.
9.
10.
11.
12.
Define a variable, 𝑠 ≤ 172
Define a variable, 𝑎 ≥ 21
(−∞, −4), Graph:
(−∞, 8], Graph:
No- provide supporting work
#3 Multi-Step Inequalities
1. a) Yes b) No
provide supporting work
2. a) Yes b) No
provide supporting work
3. 𝒙 > −7, (−𝟕, ∞), {𝑥|𝑥 > −7}
Graph:
4. 𝑛 ≤ −4, (−∞, −4], {𝑥|𝑥 ≤ −4}
Graph:
5. 𝑥 > −6, (−6, ∞), {𝑥|𝑥 > −6}
Graph:
6. 𝑥 ≤ −10, (−∞, −10], {𝑥|𝑥 ≤ −10}
Graph:
7. 𝑥 ≤ 2, (−∞, 2], {𝑥|𝑥 ≤ 2}
Graph:
8. 𝑥 ≥ 11, [11, ∞), {𝑥|𝑥 ≥ 11}
Graph:
11
#4 Writing Compound Inequalities
#5 Solving Compound Inequalities
1. Graph:
(-3, 3), {𝑥|−3 < 𝑥 < 3}
2. Graph:
(-∞, -2) or (4, ∞), {𝑥|𝑥 < −2 𝑜𝑟 𝑥 > 4}
3. Graph:
[-2, 7], {𝑥|−2 ≤ 𝑥 ≤ 7}
4. Graph:
(-5, 0], {𝑥|−5 < 𝑥 ≤ 0}
5. Graph:
(-∞, -4] or [5, ∞), {𝑥|𝑥 ≤ −4 𝑜𝑟 𝑥 ≥ 5}
6. Graph:
(-∞, -6) or [6, ∞), {𝑥|𝑥 < −6 𝑜𝑟 𝑥 ≥ 6}
7. 𝑥 < −2 𝑜𝑟 𝑥 ≥ 1, (− ∞, −2) 𝑜𝑟 [1, ∞),
{𝑥|𝑥 < −2 𝑜𝑟 𝑥 ≥ 1}
8. −3 ≤ 𝑥 ≤ 3, [−3, 3], {𝑥|−3 ≤ 𝑥 ≤ 3}
9. 𝑥 < −1 𝑜𝑟 𝑥 ≥ 3, (− ∞, −1) 𝑜𝑟 [3, ∞),
{𝑥|𝑥 < −1 𝑜𝑟 𝑥 ≥ 3}
1. 𝑦 > −2 𝑎𝑛𝑑 𝑦 ≤ 1, {𝑦|−2 < 𝑦 ≤ 1}
Graph:
2. −2 ≤ 𝑥 ≤ 5, {𝑥|−2 ≤ 𝑥 ≤ 5}
Graph:
3. 𝑣 ≤ 0 𝑜𝑟 𝑣 ≥ 10, {𝑣|𝑣 ≤ 0 𝑜𝑟 𝑣 ≥ 10}
Graph:
4. −8 < 𝑘 < −2, (−8, −2)
Graph:
5. 𝑛 > −5 𝑎𝑛𝑑 𝑛 ≤ 2, (−5, 2]
Graph:
6. 𝑛 ≤ 9 𝑜𝑟 𝑛 ≥ 10, (−∞, 9] 𝑜𝑟 [10, ∞)
Graph:
Mixed Review:
Mixed Review:
7.
8.
9.
10.
15 – 3r = 6
8 + 3k = 14
3.75 mph
7, 15
10. 𝑛 < 2, (−∞, 2), {𝑛|𝑛 > 2}
Graph:
11. 𝑦 ≥ −1, [−1, ∞), {𝑦|𝑦 ≥ −1}
Graph:
12. 𝑚 ≤ 2, (−∞, 2], {𝑚|𝑚 ≤ 2}
Graph:
12