Yahoo Answers: Answers and Comments for Inequalities and abs. value? [Mathematics]
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From Anonymous
enUS
Tue, 11 Dec 2007 16:17:28 +0000
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Yahoo Answers: Answers and Comments for Inequalities and abs. value? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
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From Any day: 3<3x4<12
3x 4 = 3x 4 when x &...
https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
Tue, 11 Dec 2007 16:33:20 +0000
3<3x4<12
3x 4 = 3x 4 when x > 4/3
3x 4 = (3x 4) when x < 4/3
3<3x4<12
a) x > 4/3 , we solve
3< 3x4 <12
let's add 4 to all term of the inequalities
3 +4 < 3x < 12 +4
7< 3x < 16
divide all term by 3 to get
7/3 < x < 16/3
b) x <4/3
we solve
3< 3x+4 <12
let's add 4 to all term of the inequalities
3 4 < 3x < 12 4
1 < 3x < 8
let's divide by (3) all terms (dividing by a negative number changes all < to > )
1/3 > x > 8/3
Summary:
a) x > 4/3
7/3 < x < 16/3 > solution domain1 =
b) x <4/3
1/3 > x > 8/3
8/3 < x < 1/3 = solution domain2
******************

From cidyah: 3<3x4<12
case 1: 3x4 >0
3x4 ...
https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
Tue, 11 Dec 2007 16:31:20 +0000
3<3x4<12
case 1: 3x4 >0
3x4 = 3x4
3x4 < 12
3x < 16
x < 16/3
3x4 >3
3x > 7
x > 7/3
7/3 < x < 16/3  (1)
case 2:
3x4 < 0
3x4 =(3x4)
=3x+4
3x+4 < 12
3x < 8
3x > 8
x > 8/3
3x+4 > 3
3x > 1
3x < 1
x < 1/3
7/3 < x < 16/3  (1)
8/3 < x < 1/3  (2)
Draw a line and see where x lies based on (1) and (2). That is your solution.

From yoda: Break off the absolute symbol by breaking the ...
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https://answers.yahoo.com/question/index?qid=20071211161728AAwU2mn
Tue, 11 Dec 2007 16:30:32 +0000
Break off the absolute symbol by breaking the inequality into its two parts. For example, x > 5 turns into x > 5 and x < 5
So:
3 < (3x 4) < 12
or
3 > (3x4) > 12
Add 4 to all sides
7 < 3x < 16
or
1 > 3x > 8
Divide by 3 to all sides. If it were 3x, you'd have to flip the inequality symbol again, but here it stays the same
7/3 < x < 16/3
or
1/3 > x > 8/3