Module 1 Lesson 4 Practice 2
(Advanced Upload of Files) Answer Key
For each of the problems (1-4) complete the following
a) Define a variable.
b) Write an absolute value inequality that represents the situation and allows
you to answer the question.
c) Solve the absolute value inequality (Show all your steps)
d) State your answer in 1-2 sentences
e) Graph your solution.
1. Your company makes bags of candy. Each bag should weigh 3 pounds. Each bag
can vary by at most 0.13 pounds. When you ship the bags of candy, you ship 5 bags
of candy in one box. What is the acceptable weight of one box?
a) 𝑤 = 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑥
b) |𝑤 − 15| ≤ 0.65
c) |𝑤 − 15| ≤ 0.65
Step 1: −0.65 ≤ 𝑤 − 15 ≤ 0.65
Step 2: 14.35 ≤ 𝑤 ≤ 15.65
d) The acceptable weight of one box of candy is 14.35 pounds to 15.65 pounds.
e)
2. When making a scarf, you try to make each scarf 4.5 feet. Each scarf can vary by
at most 4 inches. What would be the acceptable lengths of 1 scarf?
a) 𝑠 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 1 𝑠𝑐𝑎𝑟𝑓 𝑖𝑛 𝑓𝑒𝑒𝑡
1
b) |𝑠 − 4.5| ≤ 3
1
c) |𝑠 − 4.5| ≤ 3
−1
1
Step 1: 3 ≤ 𝑠 − 4.5 ≤ 3
Step 2: −1 ≤ 3𝑠 − 13.5 ≤ 1
Step 3: 12.5 ≤ 3𝑠 ≤ 14.5
25
29
1
5
Step 4: 6 ≤ 𝑠 ≤ 6
OR 4 6 ≤ 𝑠 ≤ 4 6
1
5
d) The acceptable lengths of 1 scarf would be 4 6 𝑓𝑒𝑒𝑡 to 4 6 𝑓𝑒𝑒𝑡.
e)
OR students could have used inches
a) 𝑠 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 1 𝑠𝑐𝑎𝑟𝑓 𝑖𝑛 𝑖𝑛𝑐ℎ𝑒𝑠
b) |𝑠 − 54| ≤ 4
c) |𝑠 − 54| ≤ 4
Step 1: −4 ≤ 𝑠 − 54 ≤ 4
Step 2: 50 ≤ 𝑠 ≤ 58
d) The acceptable lengths of 1 scarf would be 50 𝑖𝑛𝑐ℎ𝑒𝑠 to 58 𝑖𝑛𝑐ℎ𝑒𝑠.
e)
3. When exercising, Tracy wanted to exercise 45 minutes per day. Her exercise time
could vary by at most 15 minutes from her 45-minute goal. In a 5-day span of time,
what are the unacceptable times of exercise times?
a) 𝑒 = 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑠ℎ𝑒 𝑒𝑥𝑐𝑒𝑟𝑠𝑖𝑠𝑒𝑠 𝑖𝑛 𝑎 𝑤𝑒𝑒𝑘
b) |𝑒 − 225| > 75
c) |𝑒 − 225| > 75
Step 1: 𝑒 − 225 < −75 𝑜𝑟 𝑒 − 225 > 75
Step 2: 𝑒 < 150 𝑜𝑟 𝑒 > 300
d) The unacceptable exercise times for 5 days for Tracy are less than 150
minutes and more than 300 minutes.
e)
4. You are designing a chair and you want the width of the chair to be 24 inches.
The width can vary by at most 0.3 inches. What are the unacceptable sizes of one
chair?
a) 𝑤 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑎 𝑐ℎ𝑎𝑖𝑟
b) |𝑤 − 24| > 0.3
c) |𝑤 − 24| > 0.3
Step 1: 𝑤 − 24 < −0.3 or 𝑤 − 24 > 0.3
Step 2: 𝑤 < 23.7 or 𝑤 > 24.3
d) The unacceptable widths of the chair are widths smaller than 23.7 inches and
larger than 24.3 inches.
e)
For number 5, you are given an absolute value inequality and you have to make up a
word problem to match the absolute value inequality. For your answer you must
include at least 3 sentences. (Make sure you define the variable and express the
units)
5. |𝑥 − 140| > 30