Question

For which values of x is the inequality 3(1 + x) > x + 17 true?

A) 2 & 3
B) 4 & 5
C) 6 & 7
D) 8 & 9



5)
Solve for x.

5(x − 3) − 6(x − 2) > 8x + 2
A) x > 5/9


B) x < 5/9


C) x > −5/9


D) x < −5/9




6)
In the inequality, what are all the possible values of x?

2 − 3(2x + 1) < 6x(2 − 4)
A) x ≥ 1/6


B) x ≤ 1/6


C) x ≥ −1/6


D) x ≤ −1/6

The average normal body temperature for humans is 98.6 degrees F. An abnormal increase in body temperature is classified as hyperthermia or fever. Which inequality represents the body temperature in Celsius of a person with hyperthermia? (F = 9/5C + 32)
A) 9/5C + 32 ≥ 98.6
B) 9/5C + 32 ≤ 98.6
C) 9/5C + 32 < 98.6
D) 9/5C + 32 > 98.6




Without solving, how do you know that -5r + 6 ≤ - 10 - 5r has no solution?
A) Both variables are negative
B) The constants are different and the variables are both negative
C) The variables on both sides of the equation are equal and the constants are the same
D) The variables on both sides of the equation are equal and the constants are different

Answer 1

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.