x+5 is greater or equals to 0?

x>= -5

we change the sign from greater to smaller when take the negative sign on the opposite side
for eg

here x>= -5
we can write it as -x<=5

have you understood now??

x + 5 ≥ 0
x ≥ - 5

Answer: x ≥ - 5 or - 5 ≤ x

x + 5 ≥ 0

x ≥ - 5 is CORRECT answer (subtracting 5 from both sides )

x + 5 ≥ 0
x ≥ -5

No need to turn "greater than or equal to" to "smaller than or equal to". You can substitute some numbers that are greater than or equal to -5 for x.

it doesnt..
i believe you're geting mixed up with the steps involved in multplying by a negative number..

x + 5 > 0
x + 5 - 5 > 0 - 5
x > -5
this is true. imagine a couple of numbers that would satisfy the original inequality.. 2, 5, -4 all work, but -6 does not. trying these on the final inequality prooves that we have not made a mistake

the instance when the sign does change direction is when multiplying or dividing by a negative number:

e.g.
-6x +3 > 0
-6x +3 -3 > 0 -3
-6x > -3
now, divide both sides by NEGATIVE six, and therefor CHANGE direction of the inequality:
-6x / -6 < -3 / -6
x < 0.5

try some values to see that this is still an equivalent statement to what we had originally.

we consider all possibilities
we find x
in the first case if you have x = 5 or 1 or 2 you see the result is greater or more than zero
on the next case to get a zero x must equal to -5

It shouldn't, you need to remember that -4 is greater than -5 not less than -5. As negative numbers increase in magnitude, they decrease in value.

it doesnt turn to ''smaller or equals to" .

it remains as "greater or equals to".

it turns to "smaller or equals to" only when multiplied with an negative sign
.........