Posted by Juliette on Tuesday, October 12, 2010 at 12:18pm.
5  sqrt of 20x + 4 >= 3
5 20x + 4 >= 3
54  20x >= 3
1  20x >= 31
20x >= 4
x<= 15
Possible answers are
x<=3
1/5 <= x<= 3
x >= 1/5
x >= 0
I think it is 1/5<=x<=3
because both solutions work

AlgebraPlease check  Reiny, Tuesday, October 12, 2010 at 1:19pm
I hate to say this, but each of your lines from
5 20x + 4 >= 3
54  20x >= 3
1  20x >= 31
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

AlgebraPlease check  Juliette, Tuesday, October 12, 2010 at 3:18pm
Thank you
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