|5-3x|+3equal than or greater than 7

* Definition of the absolute value: *

* | a | = a, if a ≥ 0 *

* | a | = - a, if a < 0 *

(for example: | 5 | = 5

| -5 | = - (-5) = 5 )

**~~~~~~~~~~~~~~~**

| 5 - 3x | + 3 ≥ 7

First, let's simplify an inequality

| 5 - 3x | ≥ 7 - 3

| 5 - 3x | ≥ 4

1. Let's assume that (5 - 3x) ≥ 0 , then

5 - 3x ≥ 4

- 3x * ≥* 4 - 5 = -1

÷ (-3) ÷ (-3)

*, or any number out of*

**x ≤ 1/3**

*(- ∞, 1/3]*2. Let's assume, that (5 - 3x) is negative (< 0) , then

**–**(5 - 3x) ≥ 4

- 5 + 3x ≥ 4

3x ≥ 4 + 5 = 9

*, or any number out of*

**x ≥ 3**

**[3, ∞)**The answer is any number out of

*(- ∞, 1/3] U [3, ∞)*