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\sqrt{5x+1}-4-\left(-4\right)=-\left(-4\right)
Add 4 to both sides of the equation.
\sqrt{5x+1}=-\left(-4\right)
Subtracting -4 from itself leaves 0.
\sqrt{5x+1}=4
Subtract -4 from 0.
5x+1=16
Square both sides of the equation.
5x+1-1=16-1
Subtract 1 from both sides of the equation.
5x=16-1
Subtracting 1 from itself leaves 0.
5x=15
Subtract 1 from 16.
\frac{5x}{5}=\frac{15}{5}
Divide both sides by 5.
x=\frac{15}{5}
Dividing by 5 undoes the multiplication by 5.
x=3
Divide 15 by 5.