1.
a. 3(1 + 2) = 9; 2 + 17 = 19
9 > 19 is false so A is wrong, regardless if 3 works.
b. 3(1 + 4) = 15; 4 + 17 = 21
15 > 21 is false so we know B is wrong, regardless if 5 works.
c. 3(1 + 6) = 21; 6 + 17 = 23
21 > 23 doesn't work either.
d. 3(1 + 8) = 27; 8 + 17 = 25
27 > 25 is true. So let's test out 9.
3(1 + 9) = 30, 9 + 17 = 26
30 > 26 is also true so D is correct.
5.
Distribute: 5x-15-6x+12 > 8x +2
Simplify: -x-3 > 8x + 2
Make one side 0: 9x + 5 < 0
From there you know your answer cannot be positive or it will be above zero so A, B, and C are wrong because they all allow positive numbers at some point. So D is correct. (again)
6.
I'm not entirely sure about this one so this is my thought.
Distribute: 2 -6x - 3 < 12x -24x
Simplify: -6x -1 < -12x
Set one side to 0: 6x - 1 < 0
From there, you know the answer isn't A, B, or C because plugging in 1/6 doesn't work. So I will say that D is right as every number less than -1/6 will work.
Fahrenheit Question:
You can say that A is wrong because the equal to means that the person may be at normal temperature and not hyperthermia. That also makes B wrong as well because it too uses the equal to. C uses the less than sign (in comparison to 98.6) meaning that it looks for Celsius temperatures below the normal F temp which isn't hyperthermia. D does use the greater sign signaling that it is a temperature above the normal 98.6 So I say the answer is (again and a little fearfully) D.
Last Question:
You know their is no solution because both variables are equal but the constants are different. since -5r is equal to -5r they will ultimately cancel each other out and you'll be left with 6 is less than or equal to -10 which can never be true if the variables are the same. That means the answer is (I say very fearfully now) D.
