√(3x + 1) - 5 = 0
The first step is to collect like terms and that involves moving the constant to one side of the equation. The 5 moves to the right and becomes a positive, (when a negative value crosses to the other side of an equation it becomes a positive and vice versa).
√(3x + 1) = 5
Square both sides (to eliminate the square root sign on the left side of the equation)
3x + 1 = 25
Subtract 1 from both sides of the equation
3x + 1 - 1 = 25 - 1
3x = 24
Divide both sides of the equation by 3
x = 8
(x + 3)^2/3 - 5 = - 1
Add 5 to both sides of the equation
(x + 3)^2/3 - 5 + 5 = - 1 + 5
(x + 3)^2/3 = 4
∛(x + 3)^2 = 4
Find the cube of both sides (to eliminate the cube root sign on the left hand side)
(x + 3)^2 = 4^3
(x + 3)^2 = 64
Add the square root to both sides of the equation to eliminate the square on the left of the equation
x + 3 = √64
x + 3 = 8
Subtract 3 from both sides of the equation
x = 5