Real Numbers Worksheet

Solutions

1 Classify the following numbers:

Real Number Exercises

2 Represent the following number in the real line:: Real Number Exercises

3 Represent the numbers that verify the following relations in the real line:

|X| < 1                |x| ≤ 1              |x| > 1               |x| ≥ 1

4 Calculate the values of the following powers:

Real Number Exercises

Real Number Exercises

Real Number Exercises

Real Number Exercises

5 Represent the following number in the real line:Real Number Exercises

6Represent the following relations in the real line using real numbers:

|X −2| < 1    |x −2| ≤ 1   ; |x −2| > 1    |x −2| ≥ 1


1

Classify the following numbers:

Real Number Exercises

Real Number Solution


2

Represent the following number in the real line: Real Number Exercises

Real Number Solution

Real Line


3

Represent the numbers that verify the following relations in the real line:

|x| < 1 |x| ≤ 1 |x| > 1|x| ≥ 1

|x| < 1 −1 < x < 1  xPertenece ( −1, 1)

Representación

|x|≤ 1 −1 ≤ x ≤1 xPertenece [ −1, 1]

Representación

|x| > 1−1 > x > 1  xPertenece ( −∞, −1) Unión (1, +∞)

Representación1

|x| ≥ 1−1 ≥ x ≥ 1  xPertenece ( −∞, −1] Unión [1, +∞)

Representación


4

Calculate the values of the following powers:

Real Number Exercises

Real Number Solution

Real Number Exercises

Real Number Solution

Real Number Exercises

Real Number Solution

Real Number Exercises

Real Number Solution


5

Represent the following number in the real line: raíz

Real Number Solution

Real Line


6

Represent the following relations in the real line using real numbers:

|x −2| < 1|x −2| ≤ 1 |x −2| > 1   |x −2| ≥ 1

|x −2| < 1−1 < x −2 < 1 1 < x < 3

X Pertenece(1, 3)

Real Line

|x −2| ≤ 1−1 ≤ x −2 ≤ 11 ≤ x ≤ 3

x Pertenece [1, 3]

Real Line

|x −2| > 1 −1 > x −2 > 1 1 > x > 3

x Pertenece (-∞ , 1) Unión (3, +∞)

Real Line

|x −2| ≥ 1 −1 ≥ x −2 ≥ 11 ≥ x ≥ 3

xPertenece (-∞ , 1] Unión [3, +∞)

Real Line