## james1769 one year ago Solve the equation the square root of the quantity x + 4 - 3 equals 1 for the variable. Show each step of your solution process.

1. Michele_Laino

is your equation like this? $\sqrt {x + 4} - 3 = 1$

2. james1769

yes

3. Michele_Laino

since we have this square root $$\sqrt {x + 4}$$, then we have to request that the radical $$x+4$$ has to be greater or equal than zero: $x + 4 \geqslant 0$

4. Michele_Laino

since the square root of negative numbers doesn't exists

5. james1769

okay thanks

6. Michele_Laino

solving that inequality we have: $x \geqslant - 4$ which means that we can accept, as solutions, only those quantities which are greater or equal to -4

7. james1769

does the answer come out to be x=12

8. james1769

got one more question

9. Michele_Laino

yes! since we have to add 3 to both sides: $\sqrt {x + 4} = 4$ then squaring both sides and simplifying, we get: x=12

10. Michele_Laino

and since 12 > -4, we can conclude that x=12 is the solution of our equation

11. james1769

one more question

12. Michele_Laino

ok!