Question 165064This question is from textbook Elementary and Intermediate
: 32.)Solve each equation and check for extraneous solutions.
(3sqrt(w+1=6)
This question is from textbook Elementary and Intermediate
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! I assume that you meant to type this:
3(sqrt{w + 1}) = 6
We want to isolate the radical symbol as our first goal.
To do so, divide both sides by 3 as step one.
Doing so, we now have this radical equation:
sqrt{w + 1} = 6/3
On the right side 6/3 = 2 and so we get this:
sqrt{w + 1} = 2
To remove the radical symbol, we square both sides. In other words, raise both sides of the equation to the second power.
[sqrt{w + 1}]^2 = 2^2
w + 1 = 4
Subtract 1 from both sides.
w = 4 - 1
w = 3
WE NOW CHECK.
To check, plug w = 3 in the original question given to you and simplify.
You were given: 3(sqrt{w + 1}) = 6
Let w = 3
3(sqrt{3 + 1}) = 6
3(sqrt{4}) = 6
3(2) = 6
6 = 6....It checks!
Final answer: w = 3
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