In the next preview assignment and in the next class, you will need to label intervals on number lines and use ± notation.
Labeling Intervals on Number Lines
Suppose you want to buy a pair of jeans. At department stores, the average cost of jeans may be $30. Suppose at some stores the cost may be up to $5 over that cost, while at other stores the cost may be up to $5 lower than that cost.
We can write this using [latex]\pm[/latex] notation as $30 [latex]\pm[/latex] $5. If we subtract 5 from 30, we get $25 [latex](30 – 5 = 25)[/latex], and if we add 5 to 30, we get $35 [latex](30 + 5 = 35)[/latex].
This makes our cost range for department store jeans $25 to $35. This can be represented on a number line by putting a dot in the center at 30 and drawing a line that extends 5 in both directions.

Question 1
Suppose for a more expensive style of jeans, the average cost is $50 and the cost changes by up to $7 between stores. In other words, suppose that at some stores jeans cost up to $7 more, while in other stores jeans cost up to $7 less.
- Use the number line provided to represent the corresponding cost range for these jeans.

- Using your answer from Part a, would $63 be considered within the upper and lower bounds of the cost interval? Explain.
Question 2
Suppose you want to buy jeans somewhere a bit more expensive, where the average cost is $70. These jeans cost up to $9 more at some stores and up to $9 less at other stores.
- Use the number line provided to represent the corresponding cost range for these jeans.

- Would $75 be within the upper and lower bounds of the cost interval? Explain.
Question 3
The weight of a box of cereal filled by a machine is 16 ounces (oz). However, sometimes the box is overfilled by up to 0.5 oz, and sometimes the box is underfilled by up to 0.5 oz.
- We could represent the weight of the box of cereal (in oz) as 16 [latex]\pm[/latex] ____.
- The weight of the box of cereal filled by the machine is between ____ and _____.
- Write your answer from Part b in interval notation form, which is: (lower bound, upper bound).
Question 4
Use the number line provided to represent the interval for the weight of the box of cereal. Use a dot for the center of the interval and parentheses for the upper and lower bounds.

Question 5
Which of the following values are contained in the interval? Choose all that apply.
- 15.2
- 15.4
- 15.8
- 16.4
- 16.6
Question 6
Intervals can also be made for proportions. To answer the following questions, use the following expression: 0.35 [latex]\pm[/latex] 0.08.
- Subtract 0.08 from 0.35; we call this the lower bound.
- Add 0.35 to 0.08; we call this the upper bound.
- Plot the interval on the number line provided using a dot for the center of the interval and parentheses for the upper and lower bounds.
