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5 - sqrt of 20x + 4 >= -3
5- 20x + 4 >= -3
5-4 - 20x >= -3
1 - 20x >= -3-1
-20x >= -4
x<= -15

x<=3
-1/5 <= x<= 3
x >= -1/5
x >= 0

I think it is -1/5<=x<=3
because both solutions work

I hate to say this, but each of your lines from

5- 20x + 4 >= -3
5-4 - 20x >= -3
1 - 20x >= -3-1
-20x >= -4
x<= -15

contains an error based on its previous line

First of all , if the question is
5 - √(20x + 4) >= -3 , then
√(20x+4) ≤ 8

consider the equation

√(20x+4) = 8
square both sides
20x+4 = 64
x = 3

so we have the region > 3 and the region < 3

A quick mental consideration in √(20x+4) ≤ 8 will show that only numbers ≤ 3 could work.

finally the inside of the square root cannot be negative,
that is,
20x + 4 ≥0
x ≥ -4/20
x ≥ -1/15

so x has to be between -1/5 and 3 , or

-1/5 ≤ x ≤ 3

Thank you

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