Checking Homework: Did I Solve x Correctly?

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Homework Help Overview

The discussion revolves around solving the equation √(x+3) + 3 = 9, focusing on the interpretation of the square root and the steps taken to isolate x. The subject area is algebra, specifically dealing with irrational equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to solve the equation by isolating the square root and simplifying it, but some participants question the method used to arrive at the final value of x. Others suggest that squaring both sides could provide a clearer path to the solution.

Discussion Status

Participants are engaging in a constructive dialogue about the approach to solving the equation. While there is acknowledgment of the original poster's solution, there is also a discussion about the proper method for handling square roots and ensuring the validity of the steps taken. No explicit consensus has been reached, but guidance has been offered regarding the squaring of both sides.

Contextual Notes

There is a mention of ensuring that the expression under the square root is non-negative, which is a critical consideration in solving irrational equations. The original poster's approach has been noted as unconventional, prompting further exploration of standard methods.

LLS
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Did I do this problem correctly?

Homework Statement



The √ sign extends over x+3 only. Solve for x.

√(x+3) + 3 = 9

The Attempt at a Solution



subtract 3 from each side

√(x+3) = 6

√(33 + 3) = 6

√36 = 6

x = 33
 
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That's an odd way to solve it, but it's correct. To make things easier, you could square both sides of the equation \sqrt{x+3} = 6 and solve it easily.
 
Thank you.

I've been told that I am an odd person, LOL!

:)

Have a safe weekend.
 
Why did you input 33 as x? Well you get to the solution, but that's not how you should solve irrational equations.

\sqrt{x + 3} = 6

Until here, everything is fine but then you have to square both sides and guarantee that the expression that is under the root is not negative (which now can be excluded because we clearly see that 6 is positive, otherwise if we had a variable there, for example \sqrt{x + 3} = x + 2 can be solved by solving a system - (\sqrt{x + 3})^2 = (x + 2)^2; x + 3 \geq0)

So follows:

x + 3 = 36
x = 33I hope you can understand my explanation.EDIT: Too late
 
I understand, thank you.
 

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