Question

from unit 6, lesson 13
choose one of these inequalities to represent each situation or number line: ( x < 25 ), ( x > 25 ), ( x leq 25 ), or ( x geq 25 ).
a. the library gave a bookbag to any student who read at least 25 books over the summer. priya read ( x ) books and got a bookbag.
b. kiran read ( x ) books over the summer, but he did not get a bookbag.
c. number line with closed dot at 25 and red to the left
d. number line with open dot at 25 and red to the right
from unit 2, lesson 9
consider the problem: a water bucket is being filled with water from a water faucet at a constant rate. when will the bucket be full?
what information would you need to be able to solve the problem?

Explanation:

Step1: Match "at least 25" to inequality

"At least 25" means 25 or more, so $x \geq 25$.

Step2: Match "did not get bag" to inequality

Not getting the bag means fewer than 25 books, so $x < 25$.

Step3: Match closed dot left arrow to inequality

Closed dot at 25, arrow left means $\leq 25$, so $x \leq 25$.

Step4: Match open dot right arrow to inequality

Open dot at 25, arrow right means $>25$, so $x > 25$.

Step5: Identify needed bucket fill info

To find time to fill, need total bucket volume and fill rate.

Answer:

a. $x \geq 25$
b. $x < 25$
c. $x \leq 25$
d. $x > 25$
For the bucket problem: You would need two key pieces of information: 1) The total volume (capacity) of the water bucket, and 2) The constant rate at which water is flowing into the bucket (volume per unit time).