(14)/(x+4) is greater or equal to 2

Question

solve the rational inequality. express the solution using interval notation.

Answer 1

14/(x+4) ≥ 2 in order to solve this inequality, you have to solve system of three inequalities:
1. x ≠ -4 (we cannot divide by "0")
2. x + 4 > 0 (because 14 > 0, if you will divide by negative number result will be negative and will not satisfy given inequality) -----> x > -4
3. 14/(x+4) ≥ 2 -----> 14    ≥   2(x+4)
                                 14/2      2(x+4)/2                                     7   ≥  (x+4)
 ----> x+4 ≤ 7 ----> x ≤ 3
The answer is any number from an half of segment (-4 , 3]