How do you solve for all value of X in these two short problems:
1) X(x+1)>-1?
2) x(x^2+x+1)>-1?
Without plugging in?
1) X(x+1)>-1?
2) x(x^2+x+1)>-1?
Without plugging in?
and assign the sign-decide on inequality condition(s)/x^2+x+1=0, has no solution as D is -ve.
2) x(x^2+x+1)>-1? ----> x^3+x^2+x+1>0, (x^2 +1)(x+1)>0 /the same approach as above/ (x^2+1)(x+1)=0; x^2+1=0 OR x+1=0; x^2+1=0 ---> x doesn't have any solution as x^2 cannot be -ve and 1 is greater than 0, hence only possible x+1=0, x=-1. Plug in any value to the left from -1, x=-2 ---> (-2^2+1)(-2+1), hence x is -ve when x (-infinity;-1). Plug in any value to the right from -1, x=0 ---> (0^2+1)(0+1), hence x is +ve when x (-1; +infinity). Solution x<0 for -infinity<x<-1 and x>0 for -1<x<+infinity.
yellowho wrote:How do you solve for all value of X in these two short problems:
1) X(x+1)>-1?
2) x(x^2+x+1)>-1?
Without plugging in?
