Algebra-Please check

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

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  1. 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

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    posted by Reiny
  2. Thank you

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