james1769
  • james1769
Solve the equation the square root of the quantity x + 4 - 3 equals 1 for the variable. Show each step of your solution process.
Mathematics
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SOLVED
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katieb
  • katieb
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Michele_Laino
  • Michele_Laino
is your equation like this? \[\sqrt {x + 4} - 3 = 1\]
james1769
  • james1769
yes
Michele_Laino
  • 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: \[x + 4 \geqslant 0\]

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Michele_Laino
  • Michele_Laino
since the square root of negative numbers doesn't exists
james1769
  • james1769
okay thanks
Michele_Laino
  • 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
james1769
  • james1769
does the answer come out to be x=12
james1769
  • james1769
got one more question
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
and since 12 > -4, we can conclude that x=12 is the solution of our equation
james1769
  • james1769
one more question
Michele_Laino
  • Michele_Laino
ok!

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