SOLUTION: How do you solve 2<|x-1|<5. I am confused because i usually have only done regular absolute value inequalities, but this has two inequality signs so im confused. Thanks.
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Question 776551: How do you solve 2<|x-1|<5. I am confused because i usually have only done regular absolute value inequalities, but this has two inequality signs so im confused. Thanks.
Found 3 solutions by solver91311, stanbon, rothauserc:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Means:
OR
Note the reversal of sense in the second compound inequality. Solve the two compound inequalities and report the union of the solution sets. If you need more help on this, write back.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do you solve 2<|x-1|<5.
-----------
Note:: |x-1| has two arms, x+1 and -x-1.
You want to know for what values of "x", those arms have
y-values that are greater than 2 AND less than 5.
---------------------------------------------------
2< x-1 <5 or 2 < -(x-1) < 5
---------------------
3< x < 6 or -5< x-1 <-2
------
3< x < 6 or -4< x <-1
---------------------------
Cheers,
Stan H.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
solve 2<|x-1|<5
we have 2 cases to consider
2<|x-1| and |x-1|<5
(1) 2<|x-1|
2 < x-1
3 < x
-2 > x-1
-1 > x
so we have x>3 or x<-1
(2) |x-1|<5
x -1 < 5
x < 6
x -1 > -5
x > -4
so we have -4 < x < 6
now we need to look at where (1) and (2) overlap
-4 < x < -1 as well as 3 < x < 6
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