Which one is not an empty set? \(\displaystyle{3}{\left|{x}+{9}\right|}+{2}={1}\)

nevinijifg8

nevinijifg8

Answered question

2022-03-12

Which one is not an empty set?
3|x+9|+2=1
3|x1|211
2|x4|5<6
|3x2|4=7

Answer & Explanation

peanut13277tp

peanut13277tp

Beginner2022-03-13Added 2 answers

1) The absolute value can never be less than zero.
2) If |x|<a, a>0 then a<x<a
(a)
3|x+9|+2=1
|x+9|+2=1
3|x+9|+22=12
3|x+9|=1
3|x+9|3=13
|x+9|=13
There is no solution for xR
(b)Given:
3|x1|211
3|x1|2+211+2
3|x1|9
(3|x1|)(1)<(9)(1)
3|x1|<9
3|x1|3<93
|x1|<3
3<x1<3
x2 and x<4
2<x<4
x(2,4)
(c)
Given:
2|x4|5<6
2|x4|5<6
2|x4|5+5<6+5
2|x4|<1
2|x4|2<12
|x4|<12
There is no solution for xR
(d)
Given:
|3x2|4=7
|3x2|4=7
|3x2|4+4=7+4
|3x2|=3
There is no solution for xR
Hence the option (b) is correct.

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