Domain and absolute value

[bry32321]

Question: Where on the real axis is x defined for abs(x-5)>3? (where abs stands for the absolute value)

My work:
(x-5)<-3
x<2

(x-5)>3
x>8

so my answer is x is defined on x such that 2>x>8

Is that the correct way to express my answer or should it be x such that x<2, x>8? Or can it be either way?

 

[pka]

Question: Where on the real axis is x defined for abs(x-5)>3? (where abs stands for the absolute value)
My work:
(x-5)<-3
x<2

(x-5)>3
x>8 so my answer is x is defined on x such that 2>x>8 wrong!

Is that the correct way to express my answer or should it be x such that x<2, x>8? Or can it be either way?

The answer is written \(\displaystyle x<2\text{ or }8<x\).

In set notation \(\displaystyle (-\infty,2)\cup (8,\infty)\)

 

[bry32321]

Oh okay. Thank you very much!

 

[lookagain]

The answer is written \(\displaystyle x<2\text{ or }8<x\).

In set notation \(\displaystyle (-\infty,2)\cup (8,\infty)\)

For the first style of the answer, you will probably see it written as:

x < 2 \(\displaystyle \ or \ \) x > 8.

 

[Dale10101]

Another take

Question: Where on the real axis is x defined for abs(x-5)>3? (where abs stands for the absolute value)

My work:
(x-5)<-3
x<2

(x-5)>3
x>8

so my answer is x is defined on x such that 2>x>8

Is that the correct way to express my answer or should it be x such that x<2, x>8? Or can it be either way?

Please double click on the image and then double click on it again to see it full size.