PLEASE HELP ME!!.......INEQUALITY SOLVING: Solve and graph the solution(s). Type the solution(s) in the space provided in interval notation

Question

x² + 4x − 12 ≥ 0

  

    

 

Answer 1

If you factor the expression, you will get ( x + 6) ( x - 2 ). If both values inside the parentheses are + or - then the equality is satisfied, e.g., equal to or greater than one. If the values are opposite in sign, then the get a negative value, which does not satisfy. So on the number line mark + 2 and - 6. All values between will not satisfy and all values outside will. In interval notation we have ( - inf, - 6] U [2 . + inf) for solution.

Answer 2

Factor it fist:

(X+6)(x-2) >= 0

Mark -6 and +2 on the numeric line. You will see 3 intervals. Test one value (say 1000). You will see that the expression is positive. It will be negative between the points, and positive again on the leftmost interval

So the solution is (negative infinity, -6] union [2, positive infinity)