Math-absolute question

[Electrons]

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What value(s) does y=|2y+1|?
a) -1 only
b) -1/3 only
c) -1 or -1/3
d) 1 or 1/3
e) no values of y that satisfy this eq.

I thought it would be -1 or -1/3, that came from 2y+1=y or 2y+1 =-y respectively. However, the solution said the correct answer is E. Why?

It explains "the fact that the given equation has the abs value of a quantity equal to y immediately implies that y cannot be negative." Choice D has positive answer, why not that? Even so, how come I can say it equals to y or -y in the beginning?

 

[D.D.S.]

Hey, interesting problem. Y cant be negative since we're dealing with absolute values and also cant be 1/3 or 3. Try plugging in 3 or 1/3 for y.
Lets plug in 1/3
y=|2y+1|
y=|2(1/3)+1|
y=|5/3| = 5/3 .... but y is supposed to equal 1/3 since we plugged in 1/3 for y... so I dont think 1/3 or 3 would satisfy this equation either.

This is how I woulda approached the problem... anyone else have a better approach?

 

[deadsea]

Even so, how come I can say it equals to y or -y in the beginning?

you treat the question as |y|=2y+1 .

Making a easy question more complicate ,a common problem after practise too much. (same as me before)

 

[Streetwolf]

Try plugging in your answer... then you have a negative value 👍 = an absolute value which is by definition positive. Can't do that.

When will y = 2y+1 without y being negative? The right side of that equation will ALWAYS be > than the left if y is positive or 0. Thus the two can't equal each other unless y < 0. But then there would be no solution because the equation states that y = an absolute value, i.e. y must be >= 0.

 

[Flipper405]

Yeah... this is pretty straightforward. The negative answers don't work because anything on the right side will become positive and the left will remain negative. The positive d) 1 or 1/3 doesn't work because it just doesn't add up:
y= |2y +1|
1 x= 2(1) + 1
1/3 x= 2(1/3) + 1
I pretty much just repeated what everyone else just said... but oh well.

 

[Electrons]

Thanks all. I get it now.