Answer:
Part A : <u>|x-2.5| ≤ 0.75 , x ∈ [1.75,3.5]</u>
Part B : yes, the lifeguard should add more chlorine.
Step-by-step explanation:
Part A:
Let C is the variation of the level of chlorine in a hot tub.
Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
To find absolute value inequality, need to find the standard level of chlorine 1.75 + C or 3.25 - C
1.75 + C = 3.25 - C
2C = 5
C = 2.5
So, the standard level would be 2.5 ppm,
If x represents the present level of chlorine,
Then it would be lie within 1.75 ppm of 3.25 ppm.
1.75 ≤ x ≤ 3.25
Subtract 2.5 from all sides
1.75 - 2.5 ≤ x -2.5 ≤ 3.25 - 2.5
-0.75 ≤ (x-2.5) ≤ 0.75
which is equivalent to the following absolute value inequality.
<u>|x-2.5| ≤ 0.75</u>
<u>And the solve of the inequality : x ∈ [1.75,3.5]</u>
Part B: If x = 1.0 ppm,
∴ |1.0-2.5| = 1.5 which is not less than equal to 0.75.
Another explanation:
the minimum safe level of chlorine in a hot tub is 1.75 ppm
Since 1 < 1.75
Therefore, lifeguard should add more chlorine.
