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identify the solution of the inequality

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1 Answer

 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) 
           x ≤ 1/3 , or any number out of (- ∞, 1/3]
2. Let's assume, that (5 - 3x) is negative (< 0) , then
   (5 - 3x) ≥ 4
   - 5 + 3x ≥ 4
           3x ≥ 4 + 5 = 9
          x ≥ 3 , or any number out of [3, ∞) 

The answer is any number out of  (- ∞, 1/3] U [3, ∞)