Question

Which of the following describes the graph of x < = 1 u x > = 4?

a. closed circles on 1 and 4 with a line segment between
b. closed circles on 1 and 4 with arrows pointing outward
c. the entire number line
d. no solution

Answer 1

Closed circles on 1 and 4 with arrows pointing outward ⇒ answer b

Explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

grater than or equal b

* Now lets solve the problem

∵ {x I x ≤ 1}

∴ x is smaller than or equal 1

∵ {x I x ≥ 4}

∴ x is greater than or equal 4

∵ {x I x ≤1} ∪ {x I x ≥ 4}

- The meaning of ∪ is all numbers smaller than or equal 1 and all

the numbers greater than or equal 4

∴ {x I x ≤ 1} ∪ {x I x ≥ 4} = (-∞ , 1] ∪ [4 , ∞)

- This solution represented graphically by closed circles on 1 and

4 with arrows pointing outward

Answer 2

b. closed circles on 1 and 4 with arrows pointing outward

Explanation:

Which of the following describes the graph of x < = 1 u x ,

We have been given the following set;

x < = 1

This set comprises of real numbers that are less than or equal to 1;

(1, 0, -1, -2, -3, -4, .......... -∞)

On the other hand, the set x > = 4 comprises of real numbers that are greater than or equal to 4;

(4, 5, 6, 7, 8, 9, ........∞)

The symbol ∪ means a union of sets. That is the set of numbers that belong in either or both sets;

x < = 1 u x is same as writing;

(1, 0, -1, -2, -3, -4, .......... -∞) ∪ (4, 5, 6, 7, 8, 9, ........∞)

Therefore, the solution set will be closed circles on 1 and 4 with arrows pointing outward