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root of negative 2x plus 1 _ 3 = x
Square root of negative 2x plus 1 _ 3 + 3 = x + 3
Square root of negative 2x plus 1 = x + 3
Square root of negative 2x plus 1 _ 1 = x + 3 _ 1
Square root of negative 2 x = x + 2
(Square root of negative 2 x)2 = (x _ 4)2
_2x = x2 _ 8x + 16
_2x + 2x = x2 + 8x + 16 + 2x
0 = x2 + 10x + 16
0 = (x + 2)(x + 8)

x + 2 = 0 x + 8 = 0
x + 2 _ 2 = 0 _ 2 x + 8 _ 8 = 0

Answer :

The following errors are made:

[tex] \sqrt{-2x+1}-1=x+3-1 \\ \sqrt{-2x} =x+2[/tex] - cannot subtract 1 from radical

[tex]\sqrt{-2x} =x+2\\ \sqrt{-2x}^2 =(x-4)^2[/tex] - (x+2) should be squared

[tex]0=x^2+8x+16 \\0=(x+2)(x+6)[/tex] - incorrect factoring

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