solve this equation

[eddy2017]

 

[eddy2017]

[math]√(y-4) + 7=9[/math] ...........................................without those parentheses your work is incorrect.

subbin' 7 from both sides
[math]√(y-4) + 7 -7 =9-7[/math] ...........................................without those parentheses your work is incorrect.

[math]√(y-4) =2[/math] ...........................................without those parentheses your work is incorrect.
takin' the squares of both sides

[math]y-4=4[/math]adding 4 to both sides
[math]y=8[/math]

 

[eddy2017]

is this procedure correct?

 

[lex]

Yes

 

[eddy2017]

Yes

Thanks.

 

[lookagain]

is this procedure correct?

So far, but you need to check y = 8 in the original equation to see if it works.

 

[eddy2017]

√(y−4)+7=9
√(8−4)+7=9
√(4)+7=9
2+7=9
thanks, lookagain.

 

[lex]

Not really necessary in this case as [imath]\sqrt{y-4}=2[/imath] clearly has a solution and we have found that there is only one possible candidate, y=8, therefore it must be a/the solution.

 

[pka]

View attachment 31079

Come on Eddy. In the testing industry it is kw2one as a fifteen second question: five seconds to read & ten seconds to test each of the distractors.
[imath]\bf A.[/imath] gives a negative under the radical
[imath]\bf B.[/imath] gives a negative under the radical
[imath]\bf C.[/imath] gives a zero under the radical
[imath]\bf D.[/imath] so this is the answer. Takes a total of fifteen seconds to do.

 

[eddy2017]

Come on Eddy. In the testing industry it is kw2one as a fifteen second question: five seconds to read & ten seconds to test each of the distractors.
[imath]\bf A.[/imath] gives a negative under the radical
[imath]\bf B.[/imath] gives a negative under the radical
[imath]\bf C.[/imath] gives a zero under the radical
[imath]\bf D.[/imath] so this is the answer. Takes a total of fifteen seconds to do.

you're right. Just wanted to go ahead and performed the calculation. The more mathematics I do the more my numb mind gets a little bit more limb.

you're right. Just wanted to go ahead and performed the calculation. The more mathematics I do the more my numb mind gets a little bit more limb.

I wanted to say here that I have felt that computing numbers has a way of limbering up your mind. No matter how easy the computation.

 

[lookagain]

Not really necessary in this case as [imath]\sqrt{y-4}=2[/imath] clearly has a solution and we have found that there is only one possible candidate, y=8, therefore it must be a/the solution.

You will check any candidate solutions, because who is to say that you have not
made errors getting to other steps and ultimately to those candidate solutions.
Or, none of the solutions are correct, and the problem is found to be faulty.

 

[lex]

So far, but you need to check y = 8 in the original equation to see if it works.

You will check any candidate solutions, because who is to say that you have not
made errors getting to other steps and ultimately to those candidate solutions.
Or, none of the solutions are correct, and the problem is found to be faulty.

That's a different matter.
Yes, it is indeed good practice to check your answers and to check your working thoroughly.