Acounty government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.

Let  y represents the maximum variation in the level of chlorine,

Given,

Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.

So, the standard level of chlorine = 1.75 + y or 3.25 - y

⇒ 1.75 + y = 3.25 - y

⇒ 2y = 5

⇒ y = 2.5

Thus, 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.

If the difference between x and standard level ≤  Maximum variation

⇒ |x-2.5| ≤ 0.75

Which is the required  absolute value inequality to represent this situation.

b. If x = 1.0 ppm,

Since |1.0-2.5|=1.5 which is not less than equal to 0.75,

Hence, he should add more chlorine.

Step-by-step explanation:

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80