Verified answer

y^2 + 2y ≥ 0

y(y + 2) ≥ 0

Both factors are nonnegative or both are nonpositive.

y ≥ 0 and y + 2 ≥ 0 OR y ≤ 0 and y + 2 ≤ 0

y ≥ 0 and y ≥ -2 OR y ≤ 0 and y ≤ -2

y ≥ 0 OR y ≤ -2

Solve The Inequality For Y

y^2 + 2y >= 0

y(y + 2) >= 0

means y >= 0 or y >= - 2 since y >= - 2 covers both solutions it is the answer.

y^2 + 2y ≥ 0

Factor: y(y+2)>=0

Now locate the zeroes on a line:

Y=0 or -2

--------(-2)--------(0)------

Test (y)(y+2) in the three intervals ; you want those that make the product positive (>0)

Y<-2: choose any number: y=-10: (-)(-)=(+)****this is part of the solution

-2<y<0: try y= -1; ((-)(+)=(-)

Y> 0: try y= 10: (+)(+)=(+)***this is part of the solution

So y<=-2 or y>= 0

Hoping this helps!

factor out the "y"

y(y+2)≥ 0

y+2 ≥ 0

y ≥ -2

y ( y + 2 ) ≥ 0

_____________-2________0_________

y________-ve______-ve___0____+ve___

y + 2_____-ve__0___+ve________+ve____

product___+ve__0___-ve___0____+ve___

Sol set = { y : y ≤ -2 U y ≥ 0 }