The University of Sydney
Faculty of Economics and Business  
MathQuiz  

Inequalities - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following is the solution of  2x + 3 ≤ 9    in the real numbers?
a) x ≥ 3.    b) x ≤ 3 .
c) x ≤ 6.    d) x ≥ 6.

 

Not correct. Choice (a) is false.
Try again, if  x = 4    then  2x+ 3 = 11 > 9.
Always test your answer.
Your answer is correct.
If  2x +3 ≤ 9    then  2x ≤ 6    and  x ≤ 3.
Not correct. Choice (c) is false.
Try again, you have not solved the equation  2x + 3 = 9    correctly.
Not correct. Choice (d) is false.
Try again, you have not solved the equation  2x + 3 = 9    correctly.
Question 2 lion

Which of the following is the solution of  3 - 3x ≥ 19- x    in the real numbers?
a) x ≥ 11.    b) x ≥ - 8 .
c) x ≤ 11.    d) x ≤ - 8.

 

Not correct. Choice (a) is false.
Try again, you have not solved  3 - 3x = 19- x    correctly.
Not correct. Choice (b) is false.
Try again, remember if you multiply or divide an inequality by a negative number then you change the direction of the inequality.
Not correct. Choice (c) is false.
Try again, you have not solved  3 - 3x = 19- x    correctly.
Your answer is correct.
If  3- 3x ≥ 19 - x    then  - 2x ≥ 16    and  x ≤ - 8 .
Question 3 lion

Which of the following graphs represents  - 1 ≤ x ≤ 2?
a) PIC   b) PIC
c) PIC   d) PIC

 

Your answer is correct.
Correct, an interval of this form is always the values between the endpoints.
Not correct. Choice (b) is false.
Try again, you have  x ≤ - 1    and  x ≥ 2.
Not correct. Choice (c) is false.
Try again, you have  x ≤ 2 .
Not correct. Choice (d) is false.
Try again, you have  - 1 ≤ x.
Question 4 lion

Consider the following graph
PIC
Which statement below describes the bound on X  -axis of the shaded area?
a) 36 ≥ X ≥ 42.    b) 42 ≤ X ≤ 36 .
c) 36 ≤ X ≤ 42.    d) 42 ≥ X ≤ 36.

 

Not correct. Choice (a) is false.
Try again, this really reads X ≤ 36  or X ≥ 42 .
Not correct. Choice (b) is false.
Try again, this really reads X  ≤ 36  or X  ≥ 42.
Your answer is correct.
This reads X  ≥ 36  and X ≤ 42.
Not correct. Choice (d) is false.
Try again, this really reads X ≤ 36  and X  ≤ 42 .
Question 5 lion

Consider the following graph.
PIC
Which statement below describes the bounds and the Z  -axis and the shaded areas?
a) - 1.645 ≤ Z ≤ 1.645.    b) ∣Z ∣ ≤ 1.645.
c) - 1.645 ≤ Z ≥ 1.645.    d) ∣Z∣ ≥ 1.645.

 

Not correct. Choice (a) is false.
Try again, this is the bounds of the unshaded area on the Z  -axis.
Not correct. Choice (b) is false.
Try again, this means Z ≥ - 1.645  and Z ≤ 1.645  so this is the bounds of the unshaded area on the Z  -axis.
Not correct. Choice (c) is false.
Try again, this is just Z ≥ - 1.645.
Your answer is correct.
This means Z ≤ - 1.645  or Z ≥ 1.645.