Question

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

Answer 1

since absolute value has two solutions one positive and one negative.
\[\Large x-5\ge3\]

and
\[\Large x-5\ge-3\]
solving the first
\[\Large x \ge3+5\]
\[\Large x \ge8\]
can you solve the second equation ??
\[\Large x-5\ge-3\] ?

Answer 2

it looks strange i cnt see it. is says large x-5

Answer 3

@Pavlyunchenko

Answer 4

the whole thing change

Answer 5

are you ok with the first equation solution?

Answer 6

it wont appear as before. its like text change

Answer 7

ge-3? what is that

Answer 8

it is necessary to write as ge-3 because we have removed the absolute signs
and absolute signs have two have values jo it should be ge 3 and ge-3

Answer 9

@sami-21, your approach is not correct

Answer 10

You're too confident in your approach

Answer 11

yes i am sure .

Answer 12

| x - 5 | ≥ 3 becomes:

x - 5 ≥ 3 or x - 5 ≤ -3

Answer 13

no

Answer 14

Yes

Answer 15

I assume you think you know what the solution is

Answer 16

That's even more incorrect

Answer 17

You have the inequality signs facing the wrong way

Answer 18

If you use what I suggested, you get

\(x \le 2\)
\(x \ge 8\)

as solutions which wolframalpha confirms:

http://www.wolframalpha.com/input/?i=solve+%28%7C+x+-+5+%7C+%E2%89%A5+3%2Cx%29

Answer 19

sorry ! yes you are right

Answer 20

I arrived at my equations by using the simple rule that

\(|x-a| \ge b\) is equivalent to \(-b \ge x - a \ge b\), then separate into two equations from there:
\(x - a \ge b\)
\(x-a \le - b\)

Answer 21

yes thats corret !

Answer 22

thansk so is both the answers x - 5 ≥ 3 or x - 5 ≤ -3

Answer 23

You need to isolate x in order to find the solutions

Answer 24

srry yea is x ≥ 8 right?

Answer 25

That's one solution