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