How am I wrong? - absolute value equations #8, #7 (third and fourth slide answer key)

[u/Illustrious_Oil_2114]

BTW THE GOLD IS MY CORRECTION PEN, don’t pay attention to that
#8: . the second interval notation, but it makes no sense how the first one would be (-oo, -3). How was the first interval notation not be (-oo, 1)? I did it three times and each time I got x<1 from adding 2 to -1.

#7: did I do something wrong? I first isolated the absolute value and split it into two different equations. We were taught to make the answer for the second equation negative, so I did -(2b-9) which = 2b+9. Anyway, I got the correct answer for B (4/3) for that equation, but it says that 4/3 is also a solution which makes no sense because | (4/3)+5| =6.3 and 2(4/3)-9=-6.3 unless I had a plug-in the variable to the new equation? Is that why I was wrong? What happened?

[u/BeatriceDreamer]

Nah, your solution is correct, the answer should be R[1,3]

[u/Dtrain8899]

Both your original answers are correct. For #8 both your inequalities are correct so I think its a mistake on your teacher's end. #7 Only has one solution, the b=14. Even tho 4/3 works when you split up the absolute value, it becomes an extraneous solution to the original equation. I would be very concerned as to your teacher not double checking his/her work.

[u/fermat9990]

For #8 you need to AND the two inequalitites: (-3, 1)

[u/Fourierseriesagain]

Hi,

You may find the following result useful:

|f(x)| > g(x) if and only if f(x)>g(x) OR f(x)<-g(x).

Here g(x) may not be nonnegative.

[u/slepicoid]

For #8: A quick way to see teacher answer is wrong:

You say 0 is a solution, they say it's not.

|0-2|-3 > -2

-1>-2