#-x^2 - 9x - 16 <= - 2#
According to the law of inequality, when you multiply through with minus #(-)# sign, the inequality sign changes..
#-x^2 - 9x - 16 <= - 2#
Multiply through by #(-)#
#-(-x^2 - 9x - 16) <= -(- 2)#
Note #- xx - = +#
#x^2 + 9x + 16 >= 2#, Note that the inequality sign changes..
Collect like terms
#x^2 + 9x + 16 - 2 >= 0#
#x^2 + 9x + 14>= 0#
**Solving the Quadratic Equation, we have #7 and 2# as the factors..
Where #-> 7 xx 2 = 14, 7x + 2x = 9x#
Hence we have..
#x^2 + 9x + 14>= 0 rArr x^2 +2x +7x + 14 >=0#
#x^2 +2x +7x + 14 >=0#
#(x^2 +2x) (+7x + 14) >=0#
#x(x +2) +7 (x + 2) >=0#
#(x +2) (x + 7) >=0#
#x +2 >=0 or x + 7 >=0#
#x >=-2 or x >=-7#