# Real Numbers Worksheet

### Solutions

1 Classify the following numbers:

2 Represent the following number in the real line::

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:

5 Represent the following number in the real line:

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:

## 2

Represent the following number in the 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  x ( −1, 1)

|x|≤ 1 −1 ≤ x ≤1 x [ −1, 1]

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

1

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

## 4

Calculate the values of the following powers:

## 5

Represent the following number in the 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 (1, 3)

|x −2| ≤ 1−1 ≤ x −2 ≤ 11 ≤ x ≤ 3

x [1, 3]

|x −2| > 1 −1 > x −2 > 1 1 > x > 3

x (-∞ , 1) (3, +∞)

|x −2| ≥ 1 −1 ≥ x −2 ≥ 11 ≥ x ≥ 3

x (-∞ , 1] [3, +∞)