Question

Find the solutions of the inequality.
| x - 5 | ≥ 3

Answer 1

@E.ali @Yttrium

Answer 2

OK !
The answer off the | x - 5 | is never negative OK ?:)

Answer 3

my question Is why is it never negative?

Answer 4

Because of | | .
If each numbers come in this if they was - we have + and if + have + too !
Just this :)

Answer 5

ok understood let me try to solve it

Answer 6

It is (-infinity, 2] U [8,infinity)

Answer 7

how did you do that @Yttrium

Answer 8

Since it is | | >= 3
You need to create two inequalities
x-5 >=3 and x-5 <= -3
And this will lead you to
x >= 8 and x <= 2
And then you will form two different lines up to negative and positive infinity. Because one x must be greater than 8 and the other must be less than 2.

Answer 9

ohh ok
so how do i write it down on the paper

Answer 10

@Yttrium how do i write it down

Answer 11

You may wish to solve the related "less than" problem and remember that you are solving for what is NOT the answer.

The Answer: \(|x-5| \ge 3\)

NOT The Answer: \(|x-5| \lt 3\)

NOT the answer: The Answer: \(-3 \lt x-5 \lt 3\)

EXcluded: \(2 \lt x \lt 8\)

Answer 12

* second to last one is "NOT the answer" only. Cut and paste problem resulted in that wandering "The Answer".

Answer 13

didn't get what exactly u mean by this "Cut and paste problem resulted in that wandering "The Answer"."

Answer 14

@tkhunny didn't get what exactly u mean by this "Cut and paste problem resulted in that wandering "The Answer"."

Answer 15

The third one. It says both "NOT the answer" and "the answer". The second one should not be there.

Answer 16

ok thank you @tkhunny