workers at a hardware store take their morning break no earlier than 10AM and no later than noon.Let c represent the time the workers take their break.Write the absolute value inequality to represent the situation
hujdjcd
10 <= c <= 12
The middle time is (10+12)/2 = 11
Each extreme is only 1 away from 11, so
|c-11| <= 1
The absolute value inequality that represents the situation can be written as:
|c - 10| ≤ 2
This inequality ensures that the time, represented by c, is no earlier than 10 AM (c - 10 ≥ 0) and no later than noon (c - 12 ≤ 0). Taking the absolute value ensures that both conditions are met regardless of whether c is greater or smaller than the given limits.
To represent the given situation using absolute value inequality, we can begin by considering that the workers take their break no earlier than 10 AM and no later than noon.
Let's assume "c" represents the time the workers take their break.
Since the workers cannot take their break earlier than 10 AM, the absolute value of "c" minus 10 should be greater than or equal to zero, to ensure the time is not negative:
|c - 10| ≥ 0
Similarly, since the workers cannot take their break later than noon, the absolute value of "c" minus 12 should also be greater than or equal to zero:
|c - 12| ≥ 0
Combining both inequalities, we get:
|c - 10| ≥ 0 and |c - 12| ≥ 0
Or we can simplify it further by realizing that any real number "c" will always satisfy the condition of being greater than or equal to zero. Thus, we can write:
|c - 10| ≥ 0
This inequality indicates that the absolute difference between "c" and 10 should be greater than or equal to zero, which is always true for any value of "c".