Solve absolute value inequality. |x-1|\geq 2

killjoy1990xb9 2021-12-15 Answered
Solve absolute value inequality.
|x1|2
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Expert Answer

scoollato7o
Answered 2021-12-16 Author has 26 answers
Step 1
the given inequality is:
|x1|2
we have to solve the given inequality.
Step 2
the given inequality is |x1|2
as we know that if |x|a
then xa or xa
that implies x(,a][a,)
therefore,
|x1|2
then
x12 or x12
x12
x2+1
x1
or
x12
x2+1
x3
Step 3
therefore the solution of the given inequality is x1 or x3
that implies the solution of the given inequality is x(,1][3,)

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Donald Cheek
Answered 2021-12-17 Author has 41 answers
Step 1
The absolute value inequality is given as,
|x1|2
If an absolute inequality is given as, |f(x)|a,
|f(x)|a
={f(x)af(x)>0f(x)af(x)<0
Step 2
On solving the inequality, we get
x12
x2+1
x3...(i)
And,
x12
x2+1
x1...(ii)
Therefore, the interval for the solution of the given inequality is x(,1][3,)

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