Determine in terms of an inequalities

Inequality Calculations. See attached file for full problem description.

9.1 52.
[8x - 3(3x + 2)] - 5 ≥ 3(x + 4) - 2x

First distribute it into the parenthesis, then move x into the left side of the inequality. Remember to change the sign if a negative number is multiplied or divided.

72. Elaine's height is 67 in. Determine, in terms of an inequality, those weights W that will keep her body mass index below 25.
The body mass index is defined as

Her height is 67 inches, and BMI <25

Her weight has to be less than 159.64 pounds.

76. A long-distance telephone call using Down East Calling costs 10 cents for the first minute and 8 cents for each additional minute. The same call, placed on Long Call Systems, cost 16 cents for the first minute and 6 cents for each additional minute. For what length phone calls is Down East Calling less expensive?
Assume x minutes
The cost of long-distance call is 10 + 8(x-1)
The cost for Long call system is 16 + 6(x-1)
It is obvious x>0
So

So less than 6.5 minutes, Down east calling is less expensive.

80. Bayside Insurance offers two plans. Under plan A, Giselle would pay the first $50 of her medical bills and 20% of all bills after that. Under plan B, Giselle would pay the first $250 of bills, but only 10% of the rest. For what amount of medical bills will plan B save Giselle money? Assume that her bills will exceed $250.
Assume the medical bills is x dollars.
Then plan A: 50 + 20%(x-50) = 0.2x + 40
Place B: 250 + 10%(x-250) = 0.1x + 225
For plan B to save money, it satisfy

When the bill is over $1850, she pays less with plan B.
9.2
66. Young's rule for determining the amount of a medicine dosage for a child is given by

C = where a is the childs age and d is the usual adult dosage, in milligrams

The dosage of a medication for a 5 year old child must stay between 50mg and 100 mg. Find the equivalent adult dosage.
A= 5

So the adult dosage is between 170 mg and 340 mg.
9.3
36. |9y - 2| = 17

52. 2|2x - 7| + 11 = 25
When , , the equation can be simplified as

When , the equation is

So the solution is x = 0 or x = 7.

106. | | ≥ 1
It can be rewritten as

For

For

So the solution is