# College Algebra Problem

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Last response: in Work & Education

ECHOSIDE

May 4, 2011 6:48:26 AM

Is the number 4 a solution to √(3x+4)=-4?

I say yes, my math book says no. Here's my logic:

Finding the domain of x:

3x+4≥0

3x≥-4

x≥-(4/3)

Domain of x: [-(4/3), ∞)

√(3x+4)=-4

√(3(4)+4)=-4

√(12+4)=-4

√16=-4

-4=-4 or 4=-4

4=-4 is thrown out

-4=-4 is true, therefore x=4 is a solution to the original equation.

I appear to be misunderstanding something here. I'm sure it's simple. Can you provide any assistance?

Thanks!

I say yes, my math book says no. Here's my logic:

Finding the domain of x:

3x+4≥0

3x≥-4

x≥-(4/3)

Domain of x: [-(4/3), ∞)

√(3x+4)=-4

√(3(4)+4)=-4

√(12+4)=-4

√16=-4

-4=-4 or 4=-4

4=-4 is thrown out

-4=-4 is true, therefore x=4 is a solution to the original equation.

I appear to be misunderstanding something here. I'm sure it's simple. Can you provide any assistance?

Thanks!

More about : college algebra problem

clarkjd

May 4, 2011 1:35:47 PM

dogman_1234

May 4, 2011 1:58:28 PM

ECHOSIDE

May 5, 2011 12:57:45 PM

Dogman_1234, I'm sorry to inform you that the answer is not 2.

What must be considered here is the range of the square root operation. I did not understand that the square root symbol implies that the radical is to be solved only for the principal square root. This means that the range of the radical, when solved, is [0, ∞). No input value, x, will produce an output of -4. Therefore, x=4 is not a solution.

dogman_1234

May 5, 2011 1:55:19 PM

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