Twice a number n is no less than 10 units from -1

Question

It is an absolute value inequality 

Answer 1

Translate:
  "Twice a number n is no less than 10 units from -1"
  "The distance between -1 and 2*n is equal to or more than 10 units"
       |2n - (-1)| ≥ 10       (note: this distance is always positive; abs val)
       (2n+1) ≥ 10      or     -(2n+1) ≥ 10
        2n ≥ 9             or      -2n - 1  ≥ 10
         n ≥ 9/2           or      -2n ≥  11
         n ≥ 9/2           or      2n ≤  -11  
                  (note: multiplying by negative reverses sense of inequality)
         n ≥ 9/2           or      n ≤  -11/2
 
Checking (very important):
  Choose 10/2 = 5 as an example of n≥9/2
  Is |2(5) - (-1)| ≥ 10    ?
      | 10 + 1|  ≥ 10   ?
      | 11 | ≥ 10   ? 
       11  ≥ 10   ?  yes
  Choose -12/2 = -6 as example of n≤-11/2
  Is |2(-6) - (-1)| ≥ 10   ?
      | -12 + 1 | ≥ 10   ?
      | -11 |  ≥ 10   ?
        11 ≥ 10   ? yes
 
Ans. revised.  THX much to Mark M.